Question

In the diagram below, AB || CD, mZCHF = 119°, and mZB = 22°. Find m

Answer 1

`\angle E=39`

Step-by-step explanation

Step 1

the angle y is congruent to angle 119, so

`\angle y=119\text{ \degree}`

angle G and angle Y are vertical angles(Vertical angles are angles opposite each other where two lines cross.) and those angles are congruent

so

`\begin{gathered} \angle y=119 \\ \angle G=\angle y \\ \angle G=119 \end{gathered}`

Step 1

finally, the sum of the internal angles in a triangle equals 180, so

`\begin{gathered} \angle B+\angle G+\angle E=180 \\ replace \\ 22+119+\angle E=180 \\ 141+\angle E=180 \\ \text{subtract 141 in both sides} \\ 141+\angle E-141=180-141 \\ \angle E=39 \end{gathered}`

so, the answer is

`m\angle E=39`

I hope this helps you