Question

The measures of the angles of a quadrilateral are $(p+{25}^{\circ }),2p,(2p-{15}^{\circ })$ and $(p+{20}^{\circ })$. What is the measure of the smallest angle?

• A. ${105}^{\circ }$
• B. ${65}^{\circ }$
• C. ${115}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is D ${75}^{\circ }$

Sum of all the interior angles in a quadrilateral is ${360}^{\circ }$.

$\Rightarrow (p+{25}^{\circ })+2p+(2p-{15}^{\circ })+(p+{20}^{\circ })={360}^{\circ }$
$\Rightarrow 6p+{30}^{\circ }={360}^{\circ }$
$\Rightarrow 6p={330}^{\circ }$
$\Rightarrow p=\frac{{330}^{\circ }}{6}$
$\Rightarrow p={55}^{\circ }$
The measures of the angles are
$p+{25}^{\circ }={80}^{\circ },$
$2p={110}^{\circ },$
$2p-{15}^{\circ }={95}^{\circ },$
$p+{20}^{\circ }={75}^{\circ }$
$\therefore$ The measure of the smallest angle is ${75}^{\circ }.$