Question

∠E and ∠F are vertical angles with m∠E=8x+8 and m∠F=2x+38 . What is the value of x? Enter your answer in the box.

Answer 1

Set the two measures equal to each other. Subtract 2x from both sides and subtract 8 from both sides. Leaving you with 6x=30. Then divide 30/6 and you get X=5

Answer 2

x = 5

Explanation:

We need to remember that vertical angles are opposite to each other when two lines cross. The vertical angles that result from two lines crossing have the same measure.

In this problem we have angle E which measures 8x + 8 and angle F which measure 2x + 38.

Since they are vertical angles, we know that they have the same measure and therefore we can equal them both and solve for x:

`8x+8=2x+38\\8x-2x=38-8\\6x=30\\x=5`

Therefore, x = 5 (and ∠E = ∠F = 48)