Question

In the accompanying diagram, parallel lines AB

and CD are intersected by transversal EF at
points G and H, respectively. If the measure of
angle EGB is 3x and the measure of angle CHF
is 84, find the value of x.

Answer 1

Answer:
`x=28`

Explanation:

For this exercise you need to remember the definition of "Alternate exterior angles".

Alternate exterior angles are defined as those pairs of angles that are located outside the parallel lines and are also located on opposite sides of the transversal. They are congruent, which means that they have equal measure.

In this case you can identify in the picture given in the exercise that the angle CHF and the angle EGB are congruent (or they have equal measure). Then:

`m\angle CHF=m\angle EGB=(3x)\°=84\°`

Knowing that, you can write the following equation:

`3x=84`

Finally you can solve for "x" in order to find its value. You get that this is:

`x=(84)/(3)\\\\x=28`