Question

If one angle of a parallelogram is ${24}^{\circ }$ less than twice the smallest angle, then the measure of the largest angle of the parallelogram is

• A. ${176}^{\circ }$
• B. ${68}^{\circ }$
• C. ${112}^{\circ }$
• D. ${102}^{\circ }$

Answer 1

The correct option is C

${112}^{\circ }$

Let the smallest angle be $x$.

The largest angle = $2x-{24}^{\circ }$

But sum of two adjacent angles = ${180}^{\circ }$

$\therefore x+2x-{24}^{\circ }={180}^{\circ }\Rightarrow 3x={180}^{\circ }+24$

$\Rightarrow 3x=204\Rightarrow x=\frac{204}{3}={68}^{\circ }$

$\therefore$ Largest angle = $2x-24=2\times 68-{24}^{\circ }$

$=136-24={112}^{\circ }$