Question

In the given quadrilateral ABCD, $p^{\circ }+q^{\circ }={100}^{\circ }$,p and q are supplementary of a and b respectively
$a^{\circ }={140}^{\circ }$ and $r^{\circ }=\frac{1}{2}(a^{\circ }+q^{\circ })$ Find the angles $p^{\circ },q^{\circ }$ and $r^{\circ }$.

• A. $p=60,q=40,r=100$
• B. $p=60,q=100,r=40$
• C. $p=40,q=60,r=100$
• D. $p=100,q=60,r=120$

Answer 1

Answer: (C)

$p=40,q=60,r=100$

$p^{\circ }+a^{\circ }={180}^{\circ }$
$\Rightarrow p+{140}^{\circ }={180}^{\circ }\Rightarrow p={40}^{\circ }$

and given that $p+q={100}^{\circ }$
$\Rightarrow {40}^{\circ }+q={100}^{\circ }\Rightarrow q={60}^{\circ }$

But $b^{\circ }+q={100}^{\circ }\Rightarrow b^{\circ }+{60}^{\circ }={180}^{\circ }$
$\Rightarrow b^{\circ }={120}^{\circ }$
given $r=1/2(a+q)\Rightarrow r=1/2(140+60)$
$\Rightarrow r={100}^{\circ }$