Question

m∠xyz = 117 °
find m∠xyw and
m∠wyz .
diagram: point y with rays yz (right), yw (down), yx (left-down); angles: ∠xyw = (6x + 44)°, ∠wyz = (-10x + 65)°
m∠xyw = □ °
m∠wyz = □ °

Explanation:

Step1: Set up the angle sum equation

Since \( m\angle XYZ = m\angle XYW + m\angle WYZ \), we substitute the given expressions:
\( (6x + 44) + (-10x + 65) = 117 \)

Step2: Simplify and solve for \( x \)

Combine like terms:
\( 6x - 10x + 44 + 65 = 117 \)
\( -4x + 109 = 117 \)
Subtract 109 from both sides:
\( -4x = 117 - 109 \)
\( -4x = 8 \)
Divide by -4:
\( x = \frac{8}{-4} = -2 \)

Step3: Find \( m\angle XYW \)

Substitute \( x = -2 \) into \( 6x + 44 \):
\( 6(-2) + 44 = -12 + 44 = 32 \)

Step4: Find \( m\angle WYZ \)

Substitute \( x = -2 \) into \( -10x + 65 \):
\( -10(-2) + 65 = 20 + 65 = 85 \)

Answer:

\( m\angle XYW = \boxed{32} \)°
\( m\angle WYZ = \boxed{85} \)°