Question

1. if ∠def is a straight angle, m∠deg=(23x - 3)°, and m∠gef=(12x + 8)°. find each measure.

Explanation:

Step1: Set up equation

Since $\angle DEF$ is straight ($180^{\circ}$), $(23x - 3)+(12x + 8)=180$.

Step2: Combine like - terms

$35x+5 = 180$.

Step3: Solve for $x$

$35x=175$, so $x = 5$.

Step4: Find angle measures

$m\angle DEG=23\times5 - 3=112^{\circ}$, $m\angle GEF=12\times5 + 8 = 68^{\circ}$, $m\angle DEF = 180^{\circ}$.

Answer:

$x = 5$
$m\angle DEG=112^{\circ}$
$m\angle GEF=68^{\circ}$
$m\angle DEF = 180^{\circ}$