Question

topic 3 line and angle relationships

1. c. solve for x in each diagram.

Explanation:

Step1: Find an interior - angle related to 130°.

The interior - angle adjacent to the 130° angle forms a linear pair. So, its measure is $180 - 130=50^{\circ}$.

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 the triangle with angles $x$, 50°, and the angle adjacent to 99°. The exterior angle at $H$ is 99°. So, $x + 50=99$.

Step3: Solve for $x$.

Subtract 50 from both sides of the equation $x + 50=99$. We get $x=99 - 50=31$.

Answer:

$x = 31$