Math 1 Quiz: Triangle Angle Theorems
5 questions · exam conditions
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Triangle Angle TheoremsQuestion 1 of 5

Triangle MNPMNP has exterior angles measuring 110°110°, 125°125°, and 125°125° at vertices MM, NN, and PP respectively. What is the measure of the largest interior angle of the triangle?

55°55°
70°70°
75°75°
85°85°
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Math 1 Quiz

Math 1 Quiz: Triangle Angle Theorems

Practice Triangle Angle Theorems in Math 1 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Triangle Angle Theorems, giving you a quick way to practice the rules, question types, and explanations that matter most for Math 1.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Triangle MNPMNP has exterior angles measuring 110°110°, 125°125°, and 125°125° at vertices MM, NN, and PP respectively. What is the measure of the largest interior angle of the triangle?

  1. 55°55°
  2. 70°70° (correct answer)
  3. 75°75°
  4. 85°85°
Explanation: Each exterior angle and its corresponding interior angle are supplementary (sum to 180°180°). So the interior angles are: at MM: 180°−110°=70°180° - 110° = 70°, at NN: 180°−125°=55°180° - 125° = 55°, at PP: 180°−125°=55°180° - 125° = 55°. Let's verify: 70°+55°+55°=180°70° + 55° + 55° = 180° ✓. The largest interior angle is 70°70°. Choice (A) 55°55° gives one of the smaller interior angles. Choice (C) 75°75° and choice (D) 85°85° are incorrect calculations that don't correspond to any valid interior angle in this triangle.

Question 2

In triangle XYZXYZ, the measures of the three interior angles are in the ratio 2:3:42:3:4. If an exterior angle is drawn at the vertex corresponding to the largest interior angle, what is the measure of this exterior angle?

  1. 80°80°
  2. 100°100° (correct answer)
  3. 120°120°
  4. 140°140°
Explanation: Let the angles be 2x2x, 3x3x, and 4x4x. Using the triangle sum theorem: 2x+3x+4x=180°2x + 3x + 4x = 180°, so 9x=180°9x = 180° and x=20°x = 20°. The angles are 40°40°, 60°60°, and 80°80°. The largest interior angle is 80°80°. The exterior angle at this vertex equals the sum of the two non-adjacent interior angles: 40°+60°=100°40° + 60° = 100°. Choice (A) 80°80° incorrectly gives the measure of the largest interior angle itself. Choice (C) 120°120° would result from incorrectly adding 60°+80°60° + 80°. Choice (D) 140°140° would result from incorrectly adding 40°+80°40° + 80° and making an arithmetic error.

Question 3

In triangle RSTRST, angle R=(4y−15)°R = (4y - 15)°, angle S=(2y+25)°S = (2y + 25)°, and angle T=(y+20)°T = (y + 20)°. An exterior angle at vertex SS measures (5y+10)°(5y + 10)°. Which equation correctly represents the relationship needed to solve for yy?

  1. (4y−15)+(y+20)=(5y+10)(4y - 15) + (y + 20) = (5y + 10) (correct answer)
  2. (4y−15)+(2y+25)+(y+20)=180(4y - 15) + (2y + 25) + (y + 20) = 180
  3. (2y+25)+(5y+10)=180(2y + 25) + (5y + 10) = 180
  4. (4y−15)+(2y+25)=(5y+10)(4y - 15) + (2y + 25) = (5y + 10)
Explanation: By the exterior angle theorem, an exterior angle equals the sum of the two non-adjacent interior angles. The exterior angle at vertex SS equals the sum of angles RR and TT: (4y−15)+(y+20)=(5y+10)(4y - 15) + (y + 20) = (5y + 10). Choice (B) represents the triangle sum theorem, not the exterior angle theorem. Choice (C) incorrectly sets the interior angle at SS plus the exterior angle equal to 180°180°, which is correct but doesn't use the exterior angle theorem. Choice (D) incorrectly includes angle SS (the adjacent interior angle) instead of using only the non-adjacent angles RR and TT.

Question 4

In triangle ABC, the measure of angle A is 20° more than twice the measure of angle B, and the measure of angle C is 10° less than three times the measure of angle B. What is the measure of angle B?

  1. 25°
  2. 28° (correct answer)
  3. 30°
  4. 32°
Explanation: Let angle B measure x°. Then angle A measures (2x + 20)° and angle C measures (3x - 10)°. Using the triangle sum theorem: x + (2x + 20) + (3x - 10) = 180. Simplifying: 6x + 10 = 180, so 6x = 170, giving x = 170/6 = 85/3 ≈ 28.33°. Since the answer choices are whole numbers, we round to 28°. Check: angles are approximately 28°, 76°, and 74°, which sum to 178°, very close to 180° due to rounding.

Question 5

In triangle JKL, the ratio of the three interior angles is 2:3:42:3:4. If an exterior angle is drawn at the vertex with the smallest interior angle, what is the measure of this exterior angle?

  1. 140°140° (correct answer)
  2. 145°145°
  3. 150°150°
  4. 160°160°
Explanation: If the angles are in the ratio 2:3:42:3:4, then they can be written as 2k2k, 3k3k, and 4k4k for some value kk. Using the triangle sum theorem: 2k+3k+4k=180°2k + 3k + 4k = 180°, so 9k=180°9k = 180° and k=20°k = 20°. The three angles are 40°40°, 60°60°, and 80°80°. The smallest angle is 40°40°, so the exterior angle at that vertex is 180°−40°=140°180° - 40° = 140°.