Question

∠E and ∠F are vertical angles. If m∠E = 17p+1 and m∠F =20p-14, find m∠F.

Answer 1

The vertical angles theorem states that vertical angles are congruent to each other. Since angles E and F are vertical angles, this means you can make them equal to each other in an equation.

m∠E = m∠F

17p + 1 = 20p - 14

Subtract 20p from both sides.

-3p + 1 = -14

Subtract 1 from both sides.

-3p = -15

Divide both sides by -3.

p = 5

Substitute 5 for p in m∠F (20p - 14).

20(5) - 14 = 86

m∠F = 86°