Question

find the measure of angle d​

Answer 1

Question;

find the measure of angle d​

To find;

• angle d

Solution;

In triangle ABC,

∠CAB + ∠ABC + ∠ACB = 180° ( sum of angles in atriangleis 180° )

(a + a) + (b + b) + 55 = 180 ( ∠CAB = a + a , and ∠ACB = b + b ) refer diagram for greater understanding.

so,

2a + 2b + 55 = 180

2a + 2b = 180 - 55

2a + 2b = 125

dividing the whole equation by 2

so we get ,

a + b = 125/2..(1)

now in triangle ADC,

∠a + ∠b + ∠d = 180 ( sum of angles in a triangle is 180° )

from (1) we know the value

of a + b,

substituting it in this equation gives,

125/2 + ∠d = 180

∠d = 180 - 125/2

on cross multiplication,

∠d = (360-125)/2

∠d = 235/2

∠d = 117.5°

Concution;

the value of ∠d 117.5°.