Question

For the given diagram, the value of $m\angle QBC$ is

• A. ${50}^{\circ }$
• B. ${60}^{\circ }$
• C. ${40}^{\circ }$

Answer 1

The correct option is A ${50}^{\circ }$

For the diagram shown:
Here, we have $m\angle PAB={160}^{\circ };$
$m\angle ACR={150}^{\circ }$
Now, we know that the sum of all exterior angles of a triangle $={360}^{\circ }$
$\Rightarrow m\angle PAB+m\angle QBC+m\angle ACR={360}^{\circ }$
$\Rightarrow {160}^{\circ }+m\angle QBC+{150}^{\circ }={360}^{\circ }$
$\Rightarrow m\angle QBC={360}^{\circ }-({160}^{\circ }+{150}^{\circ })$
$\Rightarrow m\angle QBC={360}^{\circ }-{310}^{\circ }={50}^{\circ }$
$\therefore m\angle QBC={50}^{\circ }$