Question

In triangle $ABC$, the angle $C$ is six times as large as angle $A$. The measure of angle $B$ is ${60}^o$ greater than that of angle $A$. Find the measure of the angles.

• A. ${15}^o,{75}^o$ and ${90}^o$
• B. ${15}^o,{60}^o$ and ${105}^o$
• C. ${40}^o,{50}^o$ and ${90}^o$
• D. None of these

Answer 1

The correct option is A ${15}^o,{75}^o$ and ${90}^o$

Let $\angle A=x$

$\angle C=6x$

$\angle B=x+{60}^{\circ }$

Using angle sum property

$x+x+{60}^{\circ }+6x={180}^{\circ }$

$8x={120}^{\circ }$

$x={15}^{\circ }$

So the angles are

$\angle A={15}^{\circ }$

$\angle B={15}^{\circ }+{60}^{\circ }={180}^{\circ }$

$\angle C=6\times {15}^{\circ }={90}^{\circ }$