Question

h is in the interior of ∠efg. if m∠efh=(1 - 3x)°, m∠hfg=(4x + 45)°, and m∠efg=(-x + 36)°, find m∠efh.

Explanation:

Step1: Apply angle - addition postulate

$m\angle EFH + m\angle HFG=m\angle EFG$
$(1 - 3x)+(4x + 45)=-x + 36$

Step2: Simplify left - hand side

$1 - 3x+4x + 45=x + 46$
So, $x + 46=-x + 36$

Step3: Solve for x

Add x to both sides: $x+x + 46=-x+x + 36$, $2x+46 = 36$
Subtract 46 from both sides: $2x+46-46=36 - 46$, $2x=-10$
Divide both sides by 2: $x=-5$

Step4: Find $m\angle EFH$

Substitute $x = - 5$ into $m\angle EFH=(1 - 3x)^{\circ}$
$m\angle EFH=1-3\times(-5)=1 + 15=19^{\circ}$

Answer:

$19^{\circ}$