Question

if m∠efh=(5x + 1)°, m∠hfg = 62° and m∠efg=(18x + 11)°, find m∠efh

Explanation:

Step1: Use angle - addition postulate

Since $\angle EFH+\angle HFG=\angle EFG$, we have the equation $(5x + 1)+62=(18x + 11)$.

Step2: Simplify the left - hand side of the equation

$5x+1 + 62=5x+63$, so the equation becomes $5x + 63=18x+11$.

Step3: Move the terms with $x$ to one side

Subtract $5x$ from both sides: $63=18x - 5x+11$, which simplifies to $63 = 13x+11$.

Step4: Isolate the term with $x$

Subtract 11 from both sides: $63-11=13x$, so $52 = 13x$.

Step5: Solve for $x$

Divide both sides by 13: $x=\frac{52}{13}=4$.

Step6: Find the measure of $\angle EFH$

Substitute $x = 4$ into the expression for $\angle EFH$. $\angle EFH=(5x + 1)^{\circ}=(5\times4 + 1)^{\circ}=(20 + 1)^{\circ}=21^{\circ}$.

Answer:

$21^{\circ}$