Question

find the value of x.
d a c
a. 32°
b. 58°
c. 68°
d. 66°

Explanation:

Step1: Find the interior - angle at A

The angle $\angle BAD = 98^{\circ}$, and the interior - angle $\angle BAC$ and $\angle BAD$ are supplementary. So, $\angle BAC=180^{\circ}-98^{\circ}=82^{\circ}$.

Step2: Use the angle - sum property of a triangle

In $\triangle ABC$, the sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle ABC = 32^{\circ}$, $\angle BAC = 82^{\circ}$, and $\angle ACB=x^{\circ}$. Then, by the angle - sum property of a triangle $\angle ABC+\angle BAC+\angle ACB = 180^{\circ}$.
Substitute the known values: $32^{\circ}+82^{\circ}+x^{\circ}=180^{\circ}$.
Simplify the left - hand side: $114^{\circ}+x^{\circ}=180^{\circ}$.
Solve for $x$: $x^{\circ}=180^{\circ}-114^{\circ}=66^{\circ}$.

Answer:

D. $66^{\circ}$