Question

In the accompanying diagram, parallel lines AB and CD are intersected by transversal EF at G and H respectively. If measure of angle CHG equals X +20 and measure of angle DHG equals 3X find the value of X

Answer 1

The value of x can be found by setting up and solving the equation x+20=3x since angles CHG and DHG are alternate interior angles and therefore equal. Through the steps, we determine that x = 10 degrees.

The problem describes two parallel lines AB and CD intersected by a transversal EF creating angles CHG and DHG. The angles are related by the expressions x + 20 degrees and 3x degrees respectively. Since lines AB and CD are parallel, angles CHG and DHG are alternate interior angles and thus they are equal. Therefore, we can set up the equation x + 20 = 3x to find the value of x.

Steps to determine the value of x

Identify that angles CHG and DHG are equal because they are alternate interior angles.

Set up the equation x + 20 = 3x.

Simplify the equation by subtracting x from both sides to get 20 = 2x.

Divide both sides by 2 to solve for x, which gives us x = 10.

Thus, the value of x is 10 degrees.