Question

In the figure, ABCD and AEFG are parallelograms. If $\angle C={55}^{\circ }$, what is the measure of $\angle E$?
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• A. ${55}^{\circ }$
• B. ${125}^{\circ }$
• C. ${155}^{\circ }$
• D. ${35}^{\circ }$

Answer 1

The correct option is B ${125}^{\circ }$

In the parallelogram ABCD,
$\angle A=\angle C$ ....(i)
(Opposite angles of a parallelogram are equal)

In the parallelogram AEFG, GA || FE and AE is the transversal.
$\angle GAE+\angle AEF={180}^{\circ }$
(Interior angles on the same side of the transversal)

${55}^{\circ }+\angle AEF={180}^{\circ }\angle AEF={180}^{\circ }-{55}^{\circ }={125}^{\circ }\angle AEF={125}^{\circ }$