Question

h is in the interior of ∠efg. if m∠efh = (-55 + 5x)°, m∠hfg = (8x - 103)°, and m∠efg = (-8 + 3x)°, find m∠efh.

Explanation:

Step1: Apply angle - addition postulate

$m\angle EFH + m\angle HFG=m\angle EFG$
$(-55 + 5x)+(8x - 103)=-8 + 3x$

Step2: Simplify left - hand side

$(-55-103)+(5x + 8x)=-8 + 3x$
$-158+13x=-8 + 3x$

Step3: Move terms with x to one side

$13x-3x=-8 + 158$
$10x=150$

Step4: Solve for x

$x = 15$

Step5: Find m∠EFH

$m\angle EFH=-55 + 5x$
Substitute x = 15: $m\angle EFH=-55+5\times15=-55 + 75=20^{\circ}$

Answer:

$20^{\circ}$