Question

3 fill in the blank 3 points if m∠efh=(5x + 1)°, m∠hfg = 62°, and m∠efg=(18x + 11)°, find each measure. x = type your answer... m∠efh = type your answer... ° m∠efg = type your answer...

Explanation:

Step1: Use angle - addition postulate

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

Step2: Simplify the equation

$18x+11 = 5x+1 + 62$ simplifies to $18x+11=5x + 63$.

Step3: Isolate the variable terms

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

Step4: Isolate the variable

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

Step5: Solve for x

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

Step6: Find $m\angle EFH$

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

Step7: Find $m\angle EFG$

Substitute $x = 4$ into the expression for $m\angle EFG$: $m\angle EFG=(18x + 11)=(18\times4+11)=83^{\circ}$.

Answer:

$x = 4$
$m\angle EFH=21$
$m\angle EFG=83$