Question

The angles of $△ABC$ are ${30}^{\circ },{60}^{\circ }$ and ${90}^{\circ }$. Then the angles of the excentral triangle of $△ABC$ will be:

• A. ${30}^{\circ },{60}^{\circ },{90}^{\circ }$
• B. ${50}^{\circ },{65}^{\circ },{65}^{\circ }$
• C. ${35}^{\circ },{70}^{\circ },{75}^{\circ }$
• D. ${75}^{\circ },{60}^{\circ },{45}^{\circ }$

Answer 1

The correct option is D ${75}^{\circ },{60}^{\circ },{45}^{\circ }$

Let $A={30}^o,B={60}^o,C={90}^o$ be angles of $△ABC$

Then angles of excentral triangle of $△ABC$ are given by

$\frac{\pi -A}{2},\frac{\pi -B}{2},\frac{\pi -C}{2}$

$\therefore$ The angles are $\frac{{180}^o-{30}^o}{2},\frac{{180}^o-{60}^o}{2},\frac{{180}^o-{90}^o}{2}$ i.e.

$\frac{{150}^o}{2},\frac{{120}^o}{2},\frac{{90}^o}{2}={75}^o,{60}^o,{45}^o$

Hence, the angles of excentral triangle are ${75}^o,{60}^o,{45}^o$.