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

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Answer 1 · 2015-11-21T00:36:14

$52.5˚$

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 $52.5˚$ .