Question

In a $\Delta$PQR, if $\angle P-\angle Q={42}^{\circ }$ and $\angle Q-\angle R={21}^{\circ }$, find $\angle P,\angle Q$ and $\angle R$.

• A. $\angle P={105}^{\circ }\angle Q={53}^{\circ }\angle R={32}^{\circ }$
• B. $\angle P={25}^{\circ }\angle Q={53}^{\circ }\angle R={32}^{\circ }$
• C. $\angle P={95}^{\circ }\angle Q={53}^{\circ }\angle R={32}^{\circ }$
• D. $\angle P={75}^{\circ }\angle Q={53}^{\circ }\angle R={32}^{\circ }$

Answer 1

Answer: (C)

$\angle P={95}^{\circ }\angle Q={53}^{\circ }\angle R={32}^{\circ }$

Given,
$\angle P-\angle Q=42$ (I)
$\angle Q-\angle R=21$ (II)
Sum of angles = 180
$\angle P+\angle Q+\angle R=180$ (III)
Add all the three equations:
$2\angle P+\angle Q=180+42+21$
$2\angle P+\angle Q=243$ (IV)
Add I and IV,
$2\angle P+\angle P=243+42$
$3\angle P=285$
$\angle P={95}^{\circ }$
From IV, $\angle Q=243-2\times 95$
$\angle Q={53}^{\circ }$
From II,
$\angle R=53-21={32}^{\circ }$