Question

m∠ABC = (9x + 4)° and m∠DEF = (13x − 22)°. If ∠ABC and ∠DEF are supplementary, what is the measure of each angle?

Answer 1

Answer:

∠ABC measures 85° and ∠DEF measures 95°.

Step-by-step explanation:

We are given that ∠ABC and ∠DEF are supplementary. Then by definition:

$\displaystyle m\angle ABC + m\angle DE F = 180^\circ$

Substitute:

$\displaystyle \left(9x+4\right) + \left(13x-22\right) = 180$

Solve for x. Combine like terms:

$22x -18 = 180$

Add:

$\displaystyle 22x = 198$

And divide. Hence:

$\displaystyle x = 9$

To find the measure of ∠ABC, substitute and evaluate:

$\displaystyle \begin{aligned}m\angle ABC &= 9x + 4 \\ &= 9(9) + 4 \\ &= 81 + 4 \\ &= 85^\circ \end{aligned}$

And:

$\displaystyle \begin{aligned}m\ngle DE F &= 13x - 22 \\ &= 13(9) - 22 \\ &= 117-22 \\&= 95^\circ \end{aligned}$

In conclusion, ∠ABC measures 85° and ∠DEF measures 95°.