# The base angles of an isosceles triangle are congruent. If the measure of each of the base angles is twice the measure of the third angle, how do you find the measure of all three angles?

Nov 3, 2016

Base angles = $\frac{2 \pi}{5}$, Third angle = $\frac{\pi}{5}$

#### Explanation:

Let each base angle = $\theta$
Hence the third angle = $\frac{\theta}{2}$

Since the sum of the three angles must equal $\pi$
$2 \theta + \frac{\theta}{2} = \pi$

$5 \theta = 2 \pi$

$\theta = \frac{2 \pi}{5}$

$\therefore$ Third angle $= \frac{2 \pi}{5} / 2 = \frac{\pi}{5}$

Hence: Base angles = $\frac{2 \pi}{5}$, Third angle = $\frac{\pi}{5}$