Question

given g||h , what is the measure of x ?

Explanation:

Step1: Find the corresponding angle to 120°

The corresponding angle to the 120° angle formed by the trans - versal with line h has a measure of 120° because corresponding angles are equal for parallel lines g and h.

Step2: Use angle - sum property

The angle adjacent to the 80° angle and the angle corresponding to 120° and x° are in a triangle - like formation. The angle adjacent to the 80° angle is 180 - 80=100°.
We know that the sum of angles in a triangle (or the angles around a point formed by the intersection of lines) is 180°.
So, x + 100+120 = 180.
First, simplify the left - hand side: x+220 = 180.
Then, solve for x: x=180 - 220=- 40, but angles cannot be negative. We made a wrong approach above.
Let's use another property.
The alternate interior angle to the 120° angle has a measure of 120°.
The angle adjacent to the 80° angle is 100°.
We know that the sum of angles on a straight line is 180°.
The angle formed by the intersection of the non - parallel lines and the transversal related to x and the 100° angle and the angle corresponding to 120° are related as follows:
The angle corresponding to 120° and the 100° angle and x° are such that 120=100 + x.

Step3: Solve for x

Subtract 100 from both sides of the equation 120 = 100+x.
x=120 - 100
x = 20

Answer:

20