Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$3x-{40}^{\circ }+2x+{20}^{\circ }={180}^{\circ }$ [sum of adjacent angles of rhombus are equal to ${180}^{\circ }$]
$5x-{20}^{\circ }={180}^{\circ }$
$5x={180}^{\circ }+{20}^{\circ }$
$5x={200}^{\circ }$
$x=\frac{200}{5}=40$
$\Rightarrow 3x-{40}^{\circ }=3\left(40\right)-40={80}^{\circ }$
$\Rightarrow 2x+{20}^{\circ }=2\left(40\right)+20={100}^{\circ }$
The measurement of the greater angle is ${100}^{\circ }$