Question

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

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

Answer 1

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

Since two adjacent angles of a rhombus are supplementary,

We can write,

$\Rightarrow 3x-{40}^{\circ }+2x+{20}^{\circ }={180}^{\circ }$

$\Rightarrow 5x-{20}^{\circ }={180}^{\circ }$

$\Rightarrow 5x={180}^{\circ }+{20}^{\circ }$

$\Rightarrow 5x={200}^{\circ }$

$\Rightarrow x=\frac{{200}^o}{5}={40}^{\circ }$

$\therefore greaterangle=2x+{20}^{\circ }$

$=2\times {40}^{\circ }+{20}^{\circ }={100}^{\circ }$