Question

In triangle ACD, if AC is congruent to AD, measure of A = 3x-4, measure of C= 5x+1, and the measure of D = 7x-27, find x and the measure of each angle

Answer 1

AC is congruent to AD

So,

Angle C = Angle D

C= 5x+1

D = 7x-27

5x+1 = 7x-27

Solve for x:

1+27 = 7x-5x

28 = 2x

28/2 = x

x= 14

Replace x in the Angle expressions:

A = 3x-4 = 3(14)-4 = 42-4 = 38

C= 5x+1 = 5(14)+1 = 70+1 =71

D= 7x-27 = 7(14 )-27 = 98-27 = 71

A=38°

C=71°

D= 71°