Question

In the following figure, a parallelogram $EFGH$is given and $m\angle EFG=70$. Then find $m\angle HEF$.

Short answer

The measure of $m\angle HEF={110}^{\circ }$.

Step-by-step solution

Step 1. Apply the concept of a parallelogram.

In a parallelogram, the consecutive angles are supplementary.

Step 2. Check the figure.

Consider the figure.

Step 3. Step description.

Since the consecutive angles are supplementary therefore find the value of $m\angle HEF$as follows:

$\begin{array}{c}m\angle EFG+m\angle HEF={180}^{\circ }\\ {70}^{\circ }+m\angle HEF={180}^{\circ }\\ m\angle HEF={180}^{\circ }-{70}^{\circ }\\ m\angle HEF={110}^{\circ }\end{array}$

Therefore, the measure is $m\angle HEF={110}^{\circ }$.