Question

In the given figure, if $b=(2a+15{)}^{\circ }$ and $c=(3a+5{)}^{\circ }$, then the values of b and c are ___.

• A. $b={140}^{\circ }$ $c={105}^{\circ }$
• B. $b={105}^{\circ }$ $c={140}^{\circ }$
• C. $b={45}^{\circ }$ $c={105}^{\circ }$
• D. $b={105}^{\circ }$ $c={70}^{\circ }$

Answer 1

The correct option is B

$b={105}^{\circ }$

$c={140}^{\circ }$

$a+b+c+{70}^{\circ }={360}^{\circ }$ ........(sum of interior angles of a quadrilateral)

$b=(2a+15{)}^{\circ }$ .... (given)

$c=(3a+5{)}^{\circ }$ .....(given)

$\Rightarrow {70}^{\circ }+a+(2a+15)+(3a+5)={360}^{\circ }$

$\Rightarrow {70}^{\circ }+6a+{20}^{\circ }={360}^{\circ }$

$\Rightarrow 6a+{90}^{\circ }={360}^{\circ }$

$\Rightarrow 6a={360}^{\circ }-{90}^{\circ }={270}^{\circ }$

$\Rightarrow a={45}^{\circ }$

$\therefore$

$\Rightarrow b=(2a+15)=2\times 45+15$

$b=90+15={105}^{\circ }$

$\Rightarrow c=(3a+5{)}^{\circ }=3\times 45+5$

$c=135+5={140}^{\circ }$