### Student: Suresh Mehta

#### Q. If the largest angle in a triangle is 80 degrees, what is least possible value of the smallest angle of the triangle?

Hi Suresh,
Here is the solution to your question with explanation.

Topic: Geometry, Triangle
Concept: Triangle has three sides and three interior angles. The sum of the interior angles of a triangle is 180 degrees.

Method:

• Your question already provides  that the largest of the angles is  80 degrees.
• We need to find the least possible value of the smallest of the three angles.
• The least value for the smallest angle will only  be when the other two angles are as large as possible. Isn`t it Suresh?

One angle which is largest is 80 degrees as already discussed.  Now the largest value of second angle can be maximum as  80 degrees. It can not be more than 80 degrees as your already specifies largest as 80 degrees.
So taking largest value of two angles as 80 degrees each, we can easily find the smallest angle value. See below :
smallest angle + first largest angle + second largest angle = 180
Substituting value :
Smallest angle = 180 - 80 - 80

Smallest angle = 20

Hence Smallest angle = 20 degrees.
This property  The sum of the interior angles of a triangle is 180 degrees. is quite useful in solving various triangle problems.