Question

An obtuse angle of a rhombus is greater than twice the acute angle by ${30}^o$ . Find the measure of each angle.

• A. ${50}^o,{130}^o$
• B. ${60}^o,{150}^o$
• C. ${40}^o,{100}^o$
• D. ${40}^o,{110}^o$

Answer 1

The correct option is A ${50}^o,{130}^o$

Let the acute angles of the rhombus be $x$ and obtuse angles of the rhombus be $y$

Given that $y=2x+{30}^o$

We know, the sum of two adjacent angles of a rhumbus is ${180}^o$

$x+y={180}^o$

$\Rightarrow x+2x+{30}^o={180}^o$

$\Rightarrow 3x={150}^o$

$\Rightarrow x={50}^o$

So, $y=2\times {50}^o+{30}^o={130}^o$

Hence.the measure of acute angle is ${50}^o$ and the measure of obtuse angle is ${130}^o$.