# In isosceles triangle ABC, B is the vertex. The measure of angle B can be represented as (4x-2). The measure of angle A can be represented as (8x+1). Find the measure of all three angles of the triangle?

May 16, 2018

$m \angle A = 73$, $m \angle B = 34$, $m \angle C = 73$.

#### Explanation:

Since $\Delta A B C$ is an isosceles triangle, angle A is congruent to angle C.

Knowing this, and the fact that a triangle's angle measures add up to 180, we can state:

$4 x - 2 + 2 \left(8 x + 1\right) = 180$

Now solve for x.

$4 x - 2 + 16 x + 2 = 180$

$20 x = 180$

$x = 9$

Now apply x to the two given angle measures to find the new measurements.

$4 \cdot 9 - 2 = 34$

$8 \cdot 9 + 1 = 73$

$m \angle A = 73$, $m \angle B = 34$, $m \angle C = 73$.