Question

1. if ( mangle efh=(5x + 1)^{circ}), ( mangle hfg = 62^{circ}), and ( mangle efg=(18x + 11)^{circ}), find each measure.

( x=)
( mangle efh=)
( mangle efg=)

Explanation:

Step1: Use angle - addition postulate

We know that \(m\angle EFG=m\angle EFH + m\angle HFG\).
Substitute the given expressions: \((18x + 11)=(5x+1)+62\).

Step2: Solve the equation for \(x\)

Simplify the right - hand side: \((18x + 11)=5x+63\).
Subtract \(5x\) from both sides: \(18x-5x + 11=5x-5x + 63\), which gives \(13x+11 = 63\).
Subtract \(11\) from both sides: \(13x+11-11=63 - 11\), so \(13x=52\).
Divide both sides by \(13\): \(x=\frac{52}{13}=4\).

Step3: Find \(m\angle EFH\)

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

Step4: Find \(m\angle EFG\)

Substitute \(x = 4\) into \(m\angle EFG=(18x + 11)\).
\(m\angle EFG=18\times4+11=72+11 = 83^{\circ}\).

Answer:

\(x = 4\), \(m\angle EFH=21^{\circ}\), \(m\angle EFG=83^{\circ}\)