Question

Determining the Measures of Interior Angles
A segment XD is drawn in rectangle QUAD as shown below.

Rectangle Q U A D. Segment X goes from side U A to point D to form a triangle. Angle A D X is 49 degrees, and angle X A D is 90 degrees.

What are the measures of ∠XDQ and ∠UXD ?

mAngleXDQ =
°
mAngleUXD =
°

Answer 1

∠XDQ = 41°
∠UXD = 139°

Reason: In right triangle ADX, ∠XAD = 90° and ∠ADX = 49°, so ∠DXA = 180° − 90° − 49° = 41°.
∠XDQ is the complement of ∠ADX (since DA ⟂ DQ), so ∠XDQ = 90° − 49° = 41°.
∠UXD is supplementary to ∠AXD (U, X, A are collinear), so ∠UXD = 180° − 41° = 139°.