Question

One of the angles of triangle is equal to sum of the other two angles. If the ratio of the other two angles is $3:2$. Find the angles of the triangle.

• A. ${36}^o,{54}^o,{90}^o$
• B. ${45}^o,{45}^o,{90}^o$
• C. ${30}^o,{60}^o,{90}^o$
• D. None of the above.

Answer 1

The correct option is A ${36}^o,{54}^o,{90}^o$

Let one angle of the triangle be $\angle A$ and the other two triangles be $\angle B,\angle C$.

Given, one of angles of a triangle is equal to the sum of the other two triangles.

$⟹\angle A=\angle B+\angle C$

$⟹\angle A=3x+2x=5x$

Sum of 3 angles of the triangle = ${180}^o=\angle A+\angle B+\angle C$

$=5x+3x+2x$

$⟹x=18$

$\therefore \angle A=18\times 5={90}^o$

$\therefore \angle B=3\times 18={54}^o$

$\therefore \angle C=2\times 18={36}^o$