Question

$\text{Two adjacent angles of rhombus are}3x-{40}^{\circ }\text{and}2x+{20}^{\circ }.\text{Find the}\text{measurement of the greater angle.}$

• A. ${160}^{\circ }$
• B. ${100}^{\circ }$
• C. ${80}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is B ${100}^{\circ }$

The sum of the adjacent angles of a rhombus is supplementary.

So,
$3x-{40}^{\circ }+2x+{20}^{\circ }={180}^{\circ }$
$\Rightarrow 5x-{20}^{\circ }={180}^{\circ }$
$\Rightarrow 5x={200}^{\circ }$
$\Rightarrow x=\frac{{200}^{\circ }}{5}={40}^{\circ }$

$\therefore 3x-{40}^{\circ }=3\left({40}^{\circ }\right)-{40}^{\circ }={80}^{\circ }$

$2x+{20}^{\circ }=2\left({40}^{\circ }\right)+{20}^{\circ }={100}^{\circ }$

$\text{The measurement of the greater}\text{angle is}{100}^{\circ }.$