Question

Triangle ABC has angle measures as shown.

A) what is the value of x? show your work.
B) what is the measure of angle C? show your work.

Answer 1

Explanation:

(2x - 10)° + (5x + 52)° + (3x + 28)° = 180°

10x + 70 = 180

x = 11

m∠C = [ 2(11) - 10 ]° = 12°

Answer 2

12°

Explanation:

Sum of interior angles of the triangle is 180°:

m∠A + m∠B + m∠C = 180°

3x + 28° + 5x + 52° + 2x - 10° = 180°

10x + 70° = 180°

10x = 110°

x = 11°

Find the measure of angle C:

m∠C = 2x - 10° = 2(11°) - 10° = 22° - 10° = 12°