Question

In triangle ABC, m∠A=(5x−10)∘, m∠B=(12x)∘, and the exterior angle at C is (16x)∘.

What is the measure of the exterior angle at C?

Answer 1

Sum of two interiors=Exterior

• 5x-10+12x=16x
• 17x-10=16x
• 17x-16x=10
• x=10

So<C

• 16x
• 160°

Answer 2

160°

Explanation:

Sum of interior angles of a triangle = 180°

Angles on a straight line = 180°

⇒ m∠A + m∠B = exterior m∠C

⇒ (5x - 10) + (12x) = (16x)

⇒ 5x - 10 + 12x = 16x

⇒ 17x - 10 = 16x

⇒ 17x = 16x + 10

⇒ x = 10

Therefore, exterior m∠C = 16(10) = 160°