In $Δ$ $A B C$ , an exterior angle at $B$ is represented by $4 x - 2$ . If the three non-adjacent interior angles are represented by $x, 2 + x$ and $6 + 3 x$ . Find the interior and exterior angle.

Question

Q. In

Δ

A B C

, an exterior angle at

D

is represented by

X

. If the two non-adjacent interior angles are represented by

60

and

58

, find the value of

∠

X

.

Answer 1

Interior angle: sum of the angles inside

= 180^{0}

x + 2 + x + 6 + 3 x = 180

5 x + 8 = 180

5 x = 180 - 8

5 x = 172

x = 34.4

The exterior angle is equal to the sum of the two non-adjacent interior angles.

x + 4 x - 2 = 180^{o}

(sum of adjacent angles forming a straight line)

5 x = 180 - 2

5 x = 178

x = 35.6 \Rightarrow

Exterior angle

In Δ ABC, an exterior angle at B is represented by 4x−2. If the three non-adjacent interior angles are represented by x,2+x and 6+3x. Find the interior and exterior angle.