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,
[tex]\angle ACB\cong \angle DCE[/tex] (Vertically opposite angles)
[tex]m\angle ACB=m\angle DCE[/tex] (Congregant angles)
[tex]m\angle ACB=8x+4[/tex]
Using exterior angle theorem in triangle ABC, we get
[tex]m\angle A+m\angle C=\text{Exterior }m\angle B[/tex]
[tex]m\angle BAC+m\angle ACB=130^\circ[/tex]
[tex](3x-6)+(8x+4)=130^\circ[/tex]
[tex]11x-2=130^\circ[/tex]
Isolate the variable term x.
[tex]11x=130^\circ+2[/tex]
[tex]11x=132^\circ[/tex]
[tex]x=\dfrac{132^\circ}{11}[/tex]
[tex]x=12^\circ[/tex]
Now, the measure of angle A is:
[tex]m\angle A=3x-6[/tex]
[tex]m\angle A=3(12^\circ)-6[/tex]
[tex]m\angle A=36^\circ-6[/tex]
[tex]m\angle A=30^\circ[/tex]
Therefore, the correct option is B.
