Question

A utility pole makes a 90° angle with the ground. A cable wire connected to the utility pole makes an exterior angle of 110° with the ground. Using the information, find m ZXYZ.

Answer 1

Notice that angles YXW and ZXY are supplementary angles, therefore:

`\measuredangle YXW+\measuredangle ZXY=180^(\circ)`

Substituting ∡YXW=110° and solving for ∡ZXY we get:

`\measuredangle ZXY=180^(\circ)-110^(\circ)=70^(\circ)`

Also, angles XYZ and ZXY are complementary angles, then:

`\measuredangle XYZ+\measuredangle ZYX=90^(\circ)`

Substituting ∡ZXY=70° and solving for ∡XYZ we get:

`\begin{gathered} \measuredangle XYZ+70^(\circ)=90^(\circ) \\ \measuredangle XYZ=20^(\circ) \end{gathered}`