# If the largest angle of an isosceles triangle measures 106 degrees, what is the measure of the smallest angle?

Feb 11, 2016

The smallest angle is 37 degrees.

#### Explanation:

At first thought, there may be two answers

Case 1: The 106 degree angle is the vertex angle
Case 2: The 106 degree angle is a base angle

However, 106 cannot be a base angle (do you see why?)

Therefore, the 106 degree angle must be the vertex angle.

Now, we have two angles left over (the base angles) that are equal.

Since a triangle has 180 degrees in total,
$180 - 106 = 74$ for the two equal angles

Now just split the 74 into two equal angles by dividing by 2
$\frac{74}{2} = 37$

The smallest angle is therefore 37 degrees.