Question

50 POINTS! CORRECT AND EXPLANITORY ANSWERS ONLY!

Question:

Triangle ABC has angle measures as noted below.


Please note this triangle is not drawn to scale, and the longest leg of the figure may not be the longest leg of the actual triangle.


You will need to use the expressions for the angles given below.


m∠A) 3(x + 5) m∠B) 5x+15 m∠C) 7x


A. Identify the angle relationship and setup your equation with the given
expressions.


B. What is the value of x? Show your work.


C. What is the measure of angle A, B, & C? Show your work and make sure to identify which is which.

PLEASE ANSWER ALL 3 PARTS; A, B and C.

Answer 1

A) Sum of interior angles of a triangle = 180°

⇒ 3(x + 5) + 5x + 15 + 7x = 180

B) x = 10

C) m∠A = 45°

m∠B = 65°

m∠C = 70°

Explanation:

Given:

• m∠A = 3(x + 5)
• m∠B = 5x + 15
• m∠C = 7x

A) Sum of interior angles of a triangle = 180°

⇒ m∠A + m∠B + m∠C = 180

⇒ 3(x + 5) + 5x + 15 + 7x = 180

B) 3(x + 5) + 5x + 15 + 7x = 180

⇒ 3x + 15 + 5x + 15 + 7x = 180

⇒ 15x + 30 = 180

⇒ 15x = 150

⇒ x = 10

C) m∠A = 3(x + 5) = 3(10 + 5) = 3 x 15 = 45°

m∠B = 5x + 15 = (5 x 10) + 15 = 50 + 15 = 65°

m∠C = 7x = 7 x 10 = 70°