Question

If the adjacent angles of the parallelogram are $x+{30}^{\circ }$ and $2x-{90}^{\circ }$, then the smaller angle is

• A. ${110}^{\circ }$
• B. ${100}^{\circ }$
• C. ${70}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is C ${70}^{\circ }$

In a parallelogram the adjacent angles are supplementary:
$x+{30}^{\circ }+2x-{90}^{\circ }={180}^{\circ }$
$\Rightarrow 3x={240}^{\circ }$
$\Rightarrow x={80}^{\circ }$
Therefore, angles are:

$x+{30}^{\circ }={80}^{\circ }+{30}^{\circ }={110}^{\circ }$ and

$2x-{90}^{\circ }=2\times {80}^{\circ }-{90}^{\circ }={70}^{\circ }$
Therefore, smaller angle is ${70}^{\circ }$.
Option C is correct.