What is m∠1 given the following?

Question

Given: m∠1 = (5x + 21)° and m∠4 = (2x + 66)°.

The picture for this is a vertical angles theorem.

Answer 1

If angles 1 and 4 are vertical angles in the diagram, then they are congruent and have the same measure.

Set the measures of each angle equal to each other, substitute for their expressions, and solve for x:

m<1 = m<4

5x+21 = 2x+ 66

Subtracting 2x on both sides gives you: 3x +21 = 66

Subtracting 21 on both sides results in: 3x = 45

Lastly, dividing both sides by 3 gives you: x = 15.

To solve for m<1 (or m<4), substitute in 15 for x and simplify:

m<1 = 5x + 21

m<1 = 5(15)+21

m<1 = 96