Question

WXYZ is a quadrilateral in which W = 108, X =88 , Y=57 and WXZ = 31 degree. calculate WZX and XZY angle.

Answer 1

Given:

WXYZ is a quadrilateral in which W = 108°, X = 88° , Y = 57° and WXZ = 31°

To find:

Calculate WZX and XZY angle

Solution:

Finding angle WZX:

In Δ WXZ, we have

∠W + ∠WXZ + ∠WZX = 180° ...... [Angle sum property of a triangle]

substituting the given values

⇒ 108° + 31° + ∠WZX = 180°

⇒ 139° + ∠WZX = 180°

⇒ ∠WZX = 180° - 139°

⇒ ∠WZX = 41°

Thus, $\boxed{\bold{\angle WZX = 41\°}}$

Finding the angle XZY:

From the figure, we get

∠ZXY = ∠X - ∠WXZ = 88° - 31° = 57°

In Δ XYZ, we have

∠ZXY + ∠Y + ∠XZY = 180° ...... [Angle sum property of a triangle]

substituting the values of ∠Y = 57° & ∠ZXY = 57°

⇒ 57° + 57° + ∠XZY = 180°

⇒ 114° + ∠XZY = 180°

⇒ ∠XZY = 180° - 114°

⇒ ∠XZY = 66°

Thus, $\boxed{\bold{\angle XZY = 66\°}}$

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