Question

Find the value of x in each case:

Answer 1

23

Explanation:

First, we're going to solve for the angle FGE, then CGH, then we will solve for x.

A straight line has an angle of 180⁰.
180 - 78 - 14 = FGE
88 = FGE

Now we know that the angle FGE is 88⁰. Now, to solve for CGH.
180 - 88 - 78 = CGH
14 = CGH

Now we know that the angle CGH is 14⁰.

Before we solve for x, look at the graph. The lines GH and EC are parallel. This means that the angles EGH and BEC are the same degree, because they are a corresponding pair of angles, meaning they are equal.

78 + 14 = 4x
92 = 4x
23 = x

Answer 2

23°

Explanation:

We have angle BEC = angle BGH.

=> 4x = 78° + 14°

=> 4x = 92°

=> x = 23°.