Question

In the given figure:
$\angle b=2a+{15}^{\circ }$ and $\angle c=3a+5^{\circ }$, find the value of $\angle b$.

• A. ${100}^o$
• B. ${105}^o$
• C. ${95}^o$
• D. ${92}^o$

Answer 1

The correct option is B ${105}^o$

Given the angles are:

$a,{70}^o,b=2a+{15}^o$ and $c=3a+5^o$.

We know, by angle sum property, the sum of angles of a quadrilateral is ${360}^o$.

$a+b+c+{70}^o={360}^o$

$\Rightarrow a+2a+{15}^o+3a+5^o+{70}^o={360}^o$

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

$\Rightarrow 6a={270}^o$

$\Rightarrow a={45}^o$.

Therefore,

$\angle b=2a+{15}^o$

$=2\left({45}^o\right)+{15}^o$

$={90}^o+{15}^o$

$={105}^o$

Hence, option $B$ is correct.