Question

In the diagram below, ABCD is a parallelogram,AB is extended through B to E, and CE is drawn.DсABEIf CE = BE and m/D = 112°, what is mZE?Your answer

Answer 1

The opposites angle of a parallelogram are equal. So,

`\begin{gathered} \angle ABC=\angle CDA \\ \angle ABC=112 \end{gathered}`

Determine the measure of angle CBE.

`\begin{gathered} \angle CBE+\angle ABC=180 \\ \angle CBE+112=180 \\ \angle CBE=68 \end{gathered}`

Since CE = BE, so oppostie angle to side BE and CE are equal.

`\begin{gathered} \angle CBE=\angle BCE \\ \angle BCE=68 \end{gathered}`

Consider the traingle BCE.

The sum of three angles of a triangle is 180. So,

`\begin{gathered} \angle CBE+\angle BCE+\angle CEB=180 \\ 68+68+\angle CEB=180 \\ \angle CEB=180-136 \\ =44 \end{gathered}`

Thus measure of angle E is 44 degree.