Question

triangle abc is shown. the measure of the interior angle at point a is 40° and the exterior angle at point c is 102°. what is the measure of angle x? 78° 62° 118° 102°

Explanation:

Step1: Find the interior - angle at C

The exterior angle at C is 102°. The interior - angle at C and the exterior - angle at C are supplementary. Let the interior - angle at C be $\angle C$. Then $\angle C=180^{\circ}- 102^{\circ}=78^{\circ}$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In $\triangle ABC$, we know $\angle A = 40^{\circ}$ and $\angle C=78^{\circ}$. Let the interior - angle at B be $\angle B$. Then $\angle B=180^{\circ}-\angle A-\angle C=180^{\circ}-40^{\circ}-78^{\circ}=62^{\circ}$.

Step3: Find the value of x

Angle x and the interior - angle at B are supplementary. So $x = 180^{\circ}-\angle B$. Substituting $\angle B = 62^{\circ}$, we get $x=180^{\circ}-62^{\circ}=118^{\circ}$.

Answer:

118°