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98 questions across four modules, in the digital SAT’s order and on its timing, with a highlighter, a question map and a timer you can see.

A Peakscor full-length test in progress: Reading and Writing, Test A, Module 1 of 4, question 7 of 27, with the passage, four answer choices, a highlighter, a 24:18 timer and Flag, Back and Next buttons.

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Built around the real SAT blueprint.

Every question is tagged by section, domain, skill and difficulty, so you can practice exactly what you need. Full tests run like test day: two Reading & Writing modules, a break, then two Math modules.

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12 easy, 12 medium and 12 hard questions free every day, each with a full explanation. Filter by section, domain, skill and difficulty. Resets at midnight.

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Take any test on official timing, extended 1.5× time, or untimed to focus purely on accuracy.

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Four modules in official order. The second module of each section adapts to how you did on the first.

Vocabulary

1,023 essential SAT words. Browse the list, flip flashcards, or quiz yourself.

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PEAK Survivor, Hole and Peak Defense: three games powered by SAT practice questions.

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MathProblem-Solving and Data AnalysisHard

A store raises the price of a jacket by 20%. Later, it lowers the new price by 20%. The final price is what percent of the original price?

A80%
B96%Correct
C100%The trap
D104%

Check with $100: $100then$120then$96

  1. Turn each change into a multiplier.

    Up 20% means × 1.20. Down 20% means × 0.80.

  2. Apply them in order.

    1.20 × 0.80 = 0.96

  3. Read the answer.

    The final price is 96% of the original. That’s B.

  4. Why not 100%?

    The 20% cut is taken from the higher price, so it removes more than the 20% increase added.

Test day

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Every Peakscor full test follows this order. In the standard tests, the second module of each section adapts to how you did on the first.

  1. Reading & Writing · Module 1

    27 questions32 min

  2. Reading & Writing · Module 2

    27 questions32 min

    Adapts to how you did on Module 1.

  3. Break

    10 min

  4. Math · Module 1

    22 questions35 min

  5. Math · Module 2

    22 questions35 min

    Adapts to how you did on Module 1.

98 questions · 2 hr 14 min of testing, plus the break

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The Daily, plus 36 practice questions every day: 12 easy, 12 medium and 12 hard, each with a full explanation. Full-length Test A, Challenge Test 1 and all 1,023 vocabulary words are free too. No card needed.

Pro is $20 a month or $200 a year: unlimited practice with no daily limit, plus every full-length test and Challenge test. Peak is $29 a month or $280 a year: everything in Pro, plus the full Learn course and Peak Plan. Cancel anytime from your account.

98 questions across four modules, in the digital SAT’s order: Reading & Writing Module 1 and Module 2 (27 questions each), a 10-minute break, then Math Module 1 and Module 2 (22 questions each). On official timing that’s 2 hr 14 min of testing. You get estimated section scores and a total at the end.

Yes. In the standard full-length tests, Module 2 of each section is the harder version if you get 60% or more of Module 1 right, and the easier version if you don’t. Challenge tests use the hardest material throughout.

Official timing, extended 1.5× time, or untimed, on every test, including the free ones. Extended time allows 48 minutes for each Reading & Writing module and about 52 for each Math module. Untimed removes the clock so you can focus on accuracy.

A quick run with three hearts. Each right answer builds your streak: the questions get harder as it grows, and your points multiply (×2 from three in a row, ×3 from six). A miss costs a heart and drops you back to easy. Best is your longest streak.

Every day at midnight. You get a fresh 12 easy, 12 medium and 12 hard.

No. Peakscor is an independent SAT practice tool, not affiliated with the College Board. Scores shown are estimates.

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Lines, angles and triangles · Lesson 3

Triangle angles and isosceles triangles

The three angles of every triangle add up to 180∘180^\circ. This fact is on the reference sheet.

Extend one side of a triangle past a vertex and you get an exterior angle. It forms a straight line with the interior angle at that vertex, so the two add to 180∘180^\circ. It also equals the sum of the two remote interior angles, the two angles of the triangle that are not next to it. In the figure below, the exterior angle is 47+73=120∘47 + 73 = 120^\circ, and the interior angle beside it is 180−120=60∘180 - 120 = 60^\circ.

An isosceles triangle has two equal sides, often marked with matching tick marks. The angles opposite the equal sides are equal, and the reverse is true too: two equal angles mean the sides opposite them are equal. The angle at the vertex where the two equal sides meet can be different. An equilateral triangle has three equal sides and three 60∘60^\circ angles.

In any triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

The triangle inequality: each side is shorter than the sum of the other two. So if two sides are aa and bb with a≤ba \le b, the third side is greater than b−ab - a and less than a+ba + b. A third side exactly equal to b−ab - a or a+ba + b would make the three segments lie flat, not form a triangle.

An exterior angle of a triangle47°73°120°ABCD
An exterior angle of a triangle Triangle ABC with B at the bottom left, C at the bottom right and A at the top. Side BC is extended to the right past C to point D. The angle at A is labelled 47°, the angle at B is labelled 73°, and the exterior angle ACD, between CD and CA, is labelled 120°.

Worked example Easy

Two angles of a triangle measure 54∘54^\circ and 69∘69^\circ. What is the measure, in degrees, of the third angle?

  1. 5757Answer
  2. 111111
  3. 123123
  4. 126126

How to solve it

  1. The three angles add to 180∘180^\circ: 54+69+x=18054 + 69 + x = 180.
  2. 123+x=180123 + x = 180, so x=57x = 57.

Why each choice is right or wrong

  • A. Correct. 180−54−69=57180 - 54 - 69 = 57. Check: 54+69+57=18054 + 69 + 57 = 180.
  • B. Incorrect. This subtracts only the 69∘69^\circ angle, 180−69=111180 - 69 = 111, and leaves out the 54∘54^\circ angle. All three angles share the 180.
  • C. Incorrect. 123 is 54+6954 + 69, the sum of the two given angles. That sum is the exterior angle at the third vertex, not the interior angle.
  • D. Incorrect. This subtracts only the 54∘54^\circ angle, 180−54=126180 - 54 = 126, and leaves out the 69∘69^\circ angle.

Worked example Medium

Triangle ABC with side BC extended to D132°ABCD
Triangle ABC with side BC extended to D Triangle ABC with B at the bottom left, C at the bottom right and A at the top. Side BC is extended to the right past C to point D. The exterior angle ACD, between CD and CA, is labelled 132°. No other angles are labelled.

In the figure, side BCBC of triangle ABCABC is extended to point DD. The measure of angle ABCABC is 15∘15^\circ less than twice the measure of angle BACBAC. What is the measure, in degrees, of angle ABCABC?

  1. 2727
  2. 4848
  3. 4949
  4. 8383Answer

How to solve it

  1. Let angle BACBAC be x∘x^\circ. Then angle ABCABC is (2x−15)∘(2x - 15)^\circ.
  2. The exterior angle ACDACD equals the sum of the two remote interior angles, AA and BB: x+(2x−15)=132x + (2x - 15) = 132.
  3. 3x−15=1323x - 15 = 132, so 3x=1473x = 147 and x=49x = 49. Angle ABCABC is 2(49)−15=83∘2(49) - 15 = 83^\circ.
  4. Check: angle ACBACB is 180−132=48∘180 - 132 = 48^\circ, and 49+83+48=18049 + 83 + 48 = 180.

Why each choice is right or wrong

  • A. Incorrect. This treats the 132∘132^\circ angle as the third angle of the triangle: x+(2x−15)+132=180x + (2x - 15) + 132 = 180 gives 3x=633x = 63, x=21x = 21 and 2(21)−15=272(21) - 15 = 27. The 132∘132^\circ angle is outside the triangle. The interior angle at CC is 180−132=48180 - 132 = 48.
  • B. Incorrect. 48 is angle ACBACB, the interior angle at CC, 180−132180 - 132. The question asks for angle ABCABC.
  • C. Incorrect. 49 is xx, the measure of angle BACBAC. Angle ABCABC is 2(49)−15=832(49) - 15 = 83.
  • D. Correct. The exterior angle equals the sum of the remote interior angles: x+(2x−15)=132x + (2x - 15) = 132, so x=49x = 49 and angle ABCABC is 2(49)−15=83∘2(49) - 15 = 83^\circ.

Worked example Hard

Triangle ABC46°x°ABC
Triangle ABC Triangle ABC with B at the bottom left, C at the bottom right and A at the top, above a point closer to C than to B. Sides AB and BC each have one tick mark, so they are equal. The angle at B is labelled 46° and the angle at C is labelled x°.

In triangle ABCABC, AB=BCAB = BC. What is the value of xx?

  1. 4646
  2. 6767Answer
  3. 8888
  4. 134134

How to solve it

  1. The equal sides are ABAB and BCBC. The angle opposite ABAB is angle CC, and the angle opposite BCBC is angle AA. So angles AA and CC are equal, and each is x∘x^\circ.
  2. The 46∘46^\circ angle at BB is where the two equal sides meet, so it is the one angle that can be different.
  3. x+x+46=180x + x + 46 = 180, so 2x=1342x = 134 and x=67x = 67.

Why each choice is right or wrong

  • A. Incorrect. 46 assumes the two angles along the bottom side, at BB and CC, are equal. The equal angles are opposite the equal sides: ABAB is opposite angle CC and BCBC is opposite angle AA, so AA and CC are the equal pair.
  • B. Correct. Angles AA and CC are opposite the equal sides, so both are x∘x^\circ: 2x+46=1802x + 46 = 180, and x=67x = 67.
  • C. Incorrect. This makes the angles at AA and BB equal, the two ends of the marked side ABAB. Then each would be 46∘46^\circ and x=180−92=88x = 180 - 92 = 88. The equal angles are opposite the equal sides, not at the ends of one of them.
  • D. Incorrect. 134 is 180−46180 - 46, the two equal angles together. Split it between them: x=67x = 67.

Trap Pairing the wrong angles in an isosceles triangle

The equal angles are opposite the equal sides. They are not always the two angles along the bottom of the figure. Find the vertex where the two marked sides meet: the angle there is between the equal sides, and the other two angles are the equal pair.

Trap Exterior angle or interior angle

An exterior angle equals the sum of the two remote interior angles, and the interior angle beside it is its supplement. Don't add an exterior angle into the 180∘180^\circ triangle sum, and read which of the two angles the question asks for.

Trap Including the boundary in the triangle inequality

The third side must be strictly between the difference and the sum of the other two sides. A length equal to the difference or the sum gives segments that lie flat, so it can't be the third side.

Desmos When Desmos isn’t faster

Triangle angle questions are one or two subtractions, faster on paper or in your head than in Desmos.

To check arithmetic, type it on a line: 180-54-69 shows 57. When the angles are expressions in xx, graph the two sides of your equation as lines, such as y=x+(2x−15)y = x + (2x - 15) and y=132y = 132 for the exterior angle in the second example. Zoom out with the minus button at the top right of the graph until the lines cross on screen, then click the intersection, (49,132)(49, 132), to read x=49x = 49.

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Each test mirrors the digital SAT: 98 questions across four modules, 2 hr 14 min on official timing.

A little harder than the real SAT. These tests can run slightly tougher than test day, which makes them good practice: if you can handle these, the real one should feel easier. No question appears in more than one test, Challenge Tests included.

Challenge Tests Hardest of the hardest

Same 98-question format, but every question is drawn from the toughest SAT material: Challenging-tier math throughout and the hardest reading.

Vocab

Study the classic SAT vocabulary list. Browse, flip flashcards, or quiz yourself.

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