Question

angle addition postulate
find x
find m∠gfh
m∠kfh = 139°

Explanation:

Step1: Apply angle - addition postulate

According to the angle - addition postulate, \(m\angle KFH=m\angle KFG + m\angle GFH\). So, \((x + 61)+(x + 100)=139\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \(x+x+61 + 100=139\), which simplifies to \(2x+161 = 139\).

Step3: Isolate the variable term

Subtract 161 from both sides of the equation: \(2x=139 - 161\), so \(2x=-22\).

Step4: Solve for \(x\)

Divide both sides by 2: \(x=\frac{-22}{2}=-11\).

Step5: Find \(m\angle GFH\)

Substitute \(x = - 11\) into the expression for \(m\angle GFH\). \(m\angle GFH=x + 100=-11+100 = 89^{\circ}\).

Answer:

\(x=-11\)
\(m\angle GFH = 89^{\circ}\)