Question

Two consecutive angles of a parallelogram are $(x+60{)}^{\circ }\text{and}(2x+30{)}^{\circ }.$ What special name can you give to this parallelogram?

Answer 1

We know that consecutive interior angles of a parallelogram are supplementary.

$\therefore (x+60{)}^{\circ }+(2x+30{)}^{\circ }={180}^{\circ }$

$\Rightarrow 3x^{\circ }+{90}^{\circ }={180}^{\circ }$

$\Rightarrow 3x^{\circ }={90}^{\circ }$

$\Rightarrow x^{\circ }={30}^{\circ }$

Thus, two consecutive angles are $(30+60{)}^{\circ },(2\times {30}^{\circ }+{30}^{\circ })i.e.,{90}^{\circ }\text{and}{90}^{\circ }.$
Hence, the special name of the given parallelogram is rectangle.