Question

What is the measure of A

Answer 1

Given:

A figure of a triangle.

To find:

The measure of angle A.

Solution:

Label the points in the figure as shown below.

In the below figure,

$\angle ACB\cong \angle DCE$            (Vertically opposite angles)

$m\angle ACB=m\angle DCE$              (Congregant angles)

$m\angle ACB=8x+4$

Using exterior angle theorem in triangle ABC, we get

$m\angle A+m\angle C=\text{Exterior }m\angle B$

$m\angle BAC+m\angle ACB=130^\circ$

$(3x-6)+(8x+4)=130^\circ$

$11x-2=130^\circ$

Isolate the variable term x.

$11x=130^\circ+2$

$11x=132^\circ$

$x=\dfrac{132^\circ}{11}$

$x=12^\circ$

Now, the measure of angle A is:

$m\angle A=3x-6$

$m\angle A=3(12^\circ)-6$

$m\angle A=36^\circ-6$

$m\angle A=30^\circ$

Therefore, the correct option is B.