Question

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

Explanation:

Step1: Find the interior - angle at A

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

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 $\angle ACB=x$. Then $x + 32^{\circ}+82^{\circ}=180^{\circ}$.
$x=180^{\circ}-(32^{\circ}+82^{\circ})$
$x = 66^{\circ}$

Answer:

C. $66^{\circ}$