I would like to draw an isosceles triangle with the vertex measuring 75 degrees. Whats is the measure of each base angle?

1 Answer
Nov 21, 2015

#52.5˚#

Explanation:

In an isosceles triangle, there are at least #2# congruent angles—the base angles.

Here's what we know:

The vertex angle is #75˚#.
The sum of the angles in a triangle is #180˚#.
The base angles are congruent.

If we call the measure of each base angle #x#, we can write the following equation relating the degree measures of all three angles in the triangle:

#x+x+75=180#

Therefore,

#2x+75=180#
#2x=105#
#x=52.5#

So, the vertex angle of this triangle is #75˚# and each base angle is #52.5˚#.