Answer:
m∠YWZ = 36°
Step-by-step explanation:
* Lets explain how to solve the problem
- Point Y is in the interior of ∠XWZ
- Rays WX and WZ sre opposite rays
- That means rays WX and WZ formed a straight angle
- m∠XWY = 4(m∠YWZ)
- We need to find the m∠YWZ
* Lets solve the problem
∵ Rays WX and WZ are opposite rays
∴ ∠XWZ is a straight angle
∵ The measure of the straight angle is 180°
∴ m∠XWZ = 180°
- Point Y is in the interior of ∠XWZ
∴ m∠XWZ = m∠XWY + m∠YWZ
∵ m∠XWY = 180°
∴ m∠XWY + m∠YWZ = 180° ⇒ (1)
∵ m∠XWY = 4(m∠YWZ) ⇒ (2)
- Substitute equation (2) in equation (1)
- That means replace m∠XWY by 4(m∠YWZ)
∴ 4(m∠YWZ) + m∠YWZ = 180
∴ 5(m∠YWZ) = 180
- Divide both sides by 5
∴ m∠YWZ = 36°
