Question

A segment XD is drawn in rectangle QUAD as shown

Answer 1

Answer:

∠XDQ : 41°

∠UXD: 139 °

Step-by-step explanation:

Allow me to rewrite your answer for a better understanding and please have a look at the attached photo.

A segment XD is drawn in rectangle QUAD as shown  below.

What are the measures of ∠XDQ and ∠UXD ?

My answer:

As we can see in the photo, ∠ADX = 49° and ∠ADU =90°

=>  ∠XDQ = ∠ADU - ∠ADX

= 90°  - 49°  = 41°

In the triangle ADX, we can find out the angle of ∠DXA

= 180° - ∠DAX - ∠ADX

= 180° - 90° - 49°

= 41°

=> ∠UXD = 180° - ∠DXA  (Because UA is a straight line)

=180° - 41°  

= 139 °