Question

If the largest angle in a triangle is ${80}^{\circ }$, then the least possible integral value of smallest angle of the triangle is

• A. ${80}^{\circ }$
• B. ${40}^{\circ }$
• C. ${60}^{\circ }$
• D. ${21}^{\circ }$

Answer 1

Answer: (D)

${21}^{\circ }$

According to the problem :

Hence the ${180}^{\circ }$ is the sum of angle in the triangle.

Given that :

Largest angle in a triangle is ${80}^{\circ }$

Therefore,

The second largest angle is

$80-1={79}^{\circ }$ (Given that it has to integral value)

Therefore the smallest angle would be

$={180}^{\circ }-{80}^{\circ }-{70}^{\circ }$

$={21}^{\circ }$

Hence the smallest possible angle is ${21}^{\circ }$.