Question

One of the exterior angle of a triangle is ${70}^o$, interior opposite angles are in ratio $2:5$. The angles of triangle are.

• A. ${20}^o,{50}^o,{110}^o$
• B. ${70}^o,{20}^o,{90}^o$
• C. ${45}^o,{45}^o,{90}^o$
• D. ${60}^o,{60}^o,{60}^o$

Answer 1

Answer: (A)

${20}^o,{50}^o,{110}^o$

Exterior angle of a triangle is equal to the sum of opposite angles of a triangle.

Let the interior opposite angles be $2x$ and $5x$

Exterior angle of a triangle is ${70}^{\circ }$.

${70}^{\circ }=2x+5x$ .....Exterior angle property

$\Rightarrow {70}^{\circ }=7x$

$\Rightarrow x={10}^{\circ }$

Thus angles are ${20}^{\circ }$ and ${50}^{\circ }$.

Third angle is ${180}^{\circ }-{20}^{\circ }-{50}^{\circ }$ $={110}^{\circ }$.