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ACT Triangles & angles practice questions

Triangles & angles sits in the Geometry reporting category on the ACT Math section. Prep36 has 11 questions tagged to this skill, every one with a worked explanation. Three of them are below in full, with the reasoning, so you can see what the skill actually looks like before you practise it.

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What Triangles & angles covers on the ACT

Within this skill the Prep36 bank covers triangle angle sum, pythagorean theorem, supplementary angles, similar triangles & indirect measurement, parallel lines and transversals and isosceles triangle angles.

Math is 45 questions in 50 minutes, which is about 66 seconds each, and it is one of the three sections that average into your composite. The difficulty split across the 11 questions tagged here is 8 easier, 3 medium and 0 harder.

Questions are original, written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.

3 triangles & angles questions, with the reasoning

Question 1 easy

In triangle ABC, the measure of angle A is 3 times the measure of angle B, and the measure of angle C is 40°. What is the measure of the smallest angle of the triangle?

  1. A. 35° correct
  2. B. 40°
  3. C. 60°
  4. D. 105°
Why: Angles in a triangle sum to 180°, so A + B = 180° − 40° = 140°. Since A = 3B, you get 3B + B = 140°, meaning B = 35° and A = 105°. The three angles are 35°, 105°, and 40°, so the smallest is 35°. The other choices are all real quantities from the problem read in the wrong role: 105° is the largest angle, 40° is the given angle C, and 60° fits nothing here at all. Tip: after you solve for every angle, reread the last line of the question. Test writers love asking for the smallest when the biggest is what you just computed.
Question 2 medium

At a certain time of day, a person 6 feet tall casts a shadow 9 feet long. At the same time, a nearby flagpole casts a shadow 30 feet long. What is the height of the flagpole, in feet?

  1. A. 20 correct
  2. B. 27
  3. C. 45
  4. D. 180
Why: The sun hits both objects at the same angle, so the person and the flagpole form similar triangles and their height-to-shadow ratios are equal. Set up h/30 = 6/9 and solve: h = 30 × (6/9) = 20 feet. The choice 45 flips the ratio to 9/6, 27 subtracts the 3-foot gap between the person's height and shadow from 30, and 180 multiplies 6 by 30 without dividing by 9. Tip: In similar-figure problems, keep both fractions in the same order, such as height over shadow on both sides. A quick sanity check helps too: the flagpole's shadow is longer than the pole itself here, so its height must be less than 30.
Question 3 easy

In the figure below (not shown), lines l and m are parallel and are both crossed by transversal t. One of the angles formed at line l measures 68°. What is the measure of the same-side interior angle formed at line m?

  1. A. 22°
  2. B. 68°
  3. C. 122°
  4. D. 112° correct
Why: When a transversal cuts two parallel lines, same-side interior angles (also called co-interior or consecutive interior angles) are supplementary, meaning they add to 180°. So the matching angle at line m is 180° - 68° = 112°. The other three choices each apply the wrong relationship: 68° is what you would get from alternate interior or corresponding angles, which are the congruent pairs, 122° comes from subtracting from 180° after misreading the angle as 58°, and 22° uses complementary angles that sum to 90°. Tip: Memorize which parallel-line pairs are equal (alternate interior, alternate exterior, corresponding) and which are supplementary (same-side interior, same-side exterior). Naming the pair before you compute prevents almost every error on these.

The explanation is the point. Getting a question wrong tells you nothing you did not already suspect; knowing which step you missed is what changes the next one.

Practise the rest of the 11

The other 8 questions on this skill are in the free question bank, filterable by difficulty, each with the same worked explanation. No account and no card.

Open the Math bank

Frequently asked questions

How many ACT triangles & angles questions does Prep36 have?
11, each tagged to this skill and each with a worked explanation.
Are these real ACT questions?
No. They are original questions written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.
Is the Math section part of the composite?
Yes. On the Enhanced ACT the composite is the average of English, Math and Reading. Science is optional and reported separately.
Keep readingACT Math practiceEvery Math skill in one place.How many questions can you miss?The miss budget for every score.ACT Score CalculatorTurn raw scores into a composite.
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