Question

In the given figure, $\angle \theta$ is less than one-third of a right angle, then:

• A. $\varphi >{150}^{\circ }$
• B. $\varphi \ge {150}^{\circ }$
• C. $\varphi \le {150}^{\circ }$
• D. $\varphi <{150}^{\circ }$

Answer 1

The correct option is A $\varphi >{150}^{\circ }$

Given, $\theta <\frac{1}{3}$ of ${90}^{\circ }={30}^{\circ }$

But, $\theta +\varphi ={180}^{\circ }$
$\therefore \theta ={180}^{\circ }-\varphi$
$\therefore 180-\varphi <{30}^{\circ }$
or ${180}^{\circ }-{30}^{\circ }<\varphi$
or $\varphi >{150}^{\circ }$