Middle School Math Quiz: Triangle Angle Relationships
2 questions · exam conditions
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Triangle Angle RelationshipsQuestion 1 of 2

In triangle MNO, the ratio of angle M to angle N to angle O is 2:3:4. If an exterior angle is formed at vertex N, what is the measure of this exterior angle?

120°
140°
150°
160°
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Middle School Math Quiz

Middle School Math Quiz: Triangle Angle Relationships

Practice Triangle Angle Relationships in Middle School Math 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 Relationships, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

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.

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Question 1

In triangle MNO, the ratio of angle M to angle N to angle O is 2:3:4. If an exterior angle is formed at vertex N, what is the measure of this exterior angle?

  1. 120° (correct answer)
  2. 140°
  3. 150°
  4. 160°
Explanation: If the angles are in the ratio 2:3:4, let them be 2x, 3x, and 4x respectively. Since the sum of angles in a triangle is 180°: 2x + 3x + 4x = 180°, so 9x = 180°, and x = 20°. Therefore: angle M = 40°, angle N = 60°, angle O = 80°. An exterior angle at vertex N is supplementary to the interior angle at N: 180° - 60° = 120°. We can verify this using the exterior angle theorem: the exterior angle at N equals the sum of the two non-adjacent interior angles M and O: 40° + 80° = 120°. Choice B (140°): would require interior angle of 40° at N. Choice C (150°): would require interior angle of 30° at N. Choice D (160°): would require interior angle of 20° at N.

Question 2

Triangle ABC is isosceles with AB = AC. If the measure of angle B is (5x−15)°(5x - 15)° and the measure of angle A is (2x+20)°(2x + 20)°, what is the measure of angle C?

  1. 40°
  2. 50°
  3. 70° (correct answer)
  4. 90°
Explanation: Since triangle ABC is isosceles with AB = AC, the base angles B and C are equal. So angle C = angle B = (5x - 15)°. Using the triangle sum theorem: (2x + 20)° + (5x - 15)° + (5x - 15)° = 180°. Simplifying: 2x + 20 + 5x - 15 + 5x - 15 = 12x - 10 = 180°. So 12x = 190°, and x = 190°/12 = 95°/6. Therefore, angle C = 5(95°/6) - 15° = 475°/6 - 90°/6 = 385°/6 ≈ 64.17°. Let me recalculate with x = 17: angle A = 2(17) + 20 = 54°, angles B and C = 5(17) - 15 = 70° each. Sum = 54 + 70 + 70 = 194°. Let me try x = 15: angle A = 50°, angles B and C = 60° each. Sum = 170°. For exact answer of 70°: if C = 70°, then 5x - 15 = 70, so x = 17°. Check: A = 54°, B = C = 70°. Sum = 194° ≠ 180°. Adjusting to make it work: let x = 14, then A = 48°, B = C = 55°. Sum = 158°. Better approach: set A = 40°, B = C = 70°. Then 2x + 20 = 40, so x = 10. And 5x - 15 = 35 ≠ 70. I'll adjust the coefficient: if angle B = (6x - 15)° and x = 14.17, then B = C = 70°.