# If the largest angle of an isosceles triangle measures 124 degrees what is the measure of the smallest angle?

Mar 8, 2018

In an isosceles triangle, by definition two of the three sides of the triangle are equal to one another. Therefore, the angles opposite to these sides must also be equal. And considering the Triangle Sum Theorem, the angles of a triangle must add up to 180 degrees, the angle that measures 124 degrees cannot be be equal to another angle due to the fact that the sum of them would exceed 180. Therefore let x be the angle:

$124 + 2 x = 180$
$2 x = 56$
$x = 28$

The other 2 angles of the triangle must be 28 degrees each

Mar 8, 2018

$\angle A = \angle B = {28}^{\circ}$

#### Explanation:

If one angle of an isosceles triangle is greater than ${60}^{\circ}$, then the other two angles must be equal. You can use this fact and the fact that the sum of interior angles is ${180}^{\circ}$ to find the measure of those angles.

Given an isosceles triangle with $\angle C = {124}^{\circ}$, then we know know that:

$\angle A = \angle B$

And

$\angle A + \angle B + \angle C = {180}^{\circ}$

Substitute $\angle A = \angle B$:

$\angle A + \angle A + \angle C = {180}^{\circ}$

Substitute $\angle C = {124}^{\circ}$:

$2 \angle A + {124}^{\circ} = {180}^{\circ}$

$2 \angle A = {56}^{\circ}$

$\angle A = \angle B = {28}^{\circ}$