Question

1. ∠ghk is a straight angle. find m∠lhk
2. m∠xyz = 117°. find m∠xyw and m∠wyz

Explanation:

1. For the first problem:

Step1: Recall straight - angle property

A straight angle \(m\angle GHK = 180^{\circ}\).

Step2: Calculate \(m\angle LHK\)

\(m\angle LHK=180 - 79=101^{\circ}\).

1. For the second problem:

Step1: Set up the equation

Based on the angle - addition postulate \((6x + 44)+(10x+65)=117\).

Step2: Combine like - terms

\(6x+10x+44 + 65=117\), so \(16x+109 = 117\).

Step3: Solve for \(x\)

Subtract 109 from both sides: \(16x=117 - 109 = 8\), then \(x=\frac{8}{16}=\frac{1}{2}\).

Step4: Find \(m\angle XYW\)

Substitute \(x=\frac{1}{2}\) into \(6x + 44\), \(m\angle XYW=6\times\frac{1}{2}+44=47^{\circ}\).

Step5: Find \(m\angle WYZ\)

Substitute \(x=\frac{1}{2}\) into \(10x + 65\), \(m\angle WYZ=10\times\frac{1}{2}+65=70^{\circ}\).

Answer:

1. For the first problem:

• \(m\angle LHK = 101^{\circ}\)

1. For the second problem:

• First, find \(x\):
• Since \(m\angle XYZ=m\angle XYW + m\angle WYZ\), we have \((6x + 44)+(10x+65)=117\).
• Combine like - terms: \(16x+109 = 117\).
• Subtract 109 from both sides: \(16x=117 - 109=8\).
• Divide both sides by 16: \(x=\frac{8}{16}=\frac{1}{2}\).
• Then find \(m\angle XYW\) and \(m\angle WYZ\):
• \(m\angle XYW=6x + 44=6\times\frac{1}{2}+44=3 + 44 = 47^{\circ}\).
• \(m\angle WYZ=10x+65=10\times\frac{1}{2}+65=5 + 65 = 70^{\circ}\).