Question

In a quadrilateral ABCD, if $\angle A={105}^{\circ }$, $\angle B={75}^{\circ }$
and $\angle C={105}^{\circ }$, then the quadrilateral is a ____

• A. Parallelogram
• B. Rhombus
• C. Trapezium
• D. Square

Answer 1

The correct option is A

Parallelogram

$\angle A+\angle B+\angle C+\angle D={360}^{\circ }\left(Sumofanglesofaquadrilateral\right)$

${105}^{\circ }+{75}^{\circ }+{105}^{\circ }+\angle D={360}^{\circ }$

$\angle D={360}^{\circ }-({105}^{\circ }+{75}^{\circ }+{105}^{\circ })$

$\angle D={360}^{\circ }-{285}^{\circ }={75}^{\circ }$

$\angle D={75}^{\circ }$

As the opposite angles are equal, the quadrilateral ABCD is a parallelogram.