Question

What is the measure of Zx? Angles are not necessarily drawn to scale.

Answer 1

Answer:

This question is straightforward if you find different triangles in the figure itself.

Property of a triangle: All internal angles of a triangle must add up to 180°

Take a look at Triangle DBH.

Method A

Angle BHD = 180°-33°-46° (sum of angles in a triangle)

                   = 101°

Property of angles on a straight line: All angles on a straight line must add up to 180°

Angle x = 180°-101° (supplementary angles)

             = 79°

Method B

Take a look at Triangle DBH.

Property of exterior angle (in this case, angle x): An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.

Angle x = 33°+46°

             = 79°