Question

c. solve for x in each diagram. 1.

Explanation:

Step1: Find the exterior - angle adjacent to 130°.

The exterior - angle adjacent to 130° and 130° are supplementary. Let the adjacent exterior - angle be $y$. Then $y + 130^{\circ}=180^{\circ}$, so $y = 180^{\circ}-130^{\circ}=50^{\circ}$.

Step2: Use the exterior - angle property of a triangle.

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. In $\triangle GFH$, the exterior - angle at $H$ is 99°. So, $99^{\circ}=x + 50^{\circ}$.

Step3: Solve for $x$.

Subtract 50° from both sides of the equation $99^{\circ}=x + 50^{\circ}$. We get $x=99^{\circ}-50^{\circ}=49^{\circ}$.

Answer:

$49^{\circ}$