Question

In Fig, if a is greater than b by one third of a right angle. Find the values of a and b.

Answer 1

Hint: In general the value of a straight line angle is ${{180}^{\circ }}$ and value of right line angle is ${{90}^{\circ }}$.

Complete step-by-step solution -
As given a is greater than b by one third of a right angle.
As we know the value of the right angle is ${{90}^{\circ }}$.
So one third of right angle is $\dfrac{{{90}^{\circ }}}{3}={{30}^{\circ }}$
So we can write
$\Rightarrow a=b+{{30}^{\circ }}$……………...……………………(i)
In general the value of straight line angle is ${{180}^{\circ }}$.
So we can write
$a+b={{180}^{\circ }}$
From equation (i) we can write value of a
$\Rightarrow b+{{30}^{\circ }}+b={{180}^{\circ }}$
$\Rightarrow 2b+{{30}^{\circ }}={{180}^{\circ }}$
$\Rightarrow 2b={{180}^{\circ }}-{{30}^{\circ }}$
$\Rightarrow 2b={{150}^{\circ }}$
$\Rightarrow b=\dfrac{{{150}^{\circ }}}{2}$
$\Rightarrow b={{75}^{\circ }}$
From equation (i)
$a={{75}^{\circ }}+{{30}^{\circ }}={{105}^{\circ }}$
Hence the value of a is ${{105}^{\circ }}$and b is ${{75}^{\circ }}$ .

Note: While solving this question we need to be careful that a is greater than b. So we will add one third of the right angle in b. Here angle b is acute angle, so we can conclude that angle a will be obtuse angle. Hence the value of angle a is greater than ${90}^\circ$.