# In isosceles ABC, B is the vertex. The measure of angle B can be represented as (8x+2). The measure of angle A can be represented as (9x-2). Find the measure of all three angles of the triangle. Be sure to name the angle with it’s measurement (ex: angle A= ).

## two angles are the same (given it is isoslese)

the angles add up to 180 degrees

use this to answer the question

## find x

and then plug x in to find respective angles

## To find the measure of all three angles of the isosceles triangle ABC, we can use the fact that the sum of the angles in any triangle is always 180 degrees.

Let's start by labeling the angles:

Angle B = 8x + 2 (Given)
Angle A = 9x - 2 (Given)
Angle C = Other angle of the triangle

Since ABC is an isosceles triangle, angle A and angle C are congruent. This means they have the same measure. So we can set up an equation:

Angle A + Angle C + Angle B = 180

Replacing the values of angle A and angle B:

(9x - 2) + (9x - 2) + (8x + 2) = 180

Combine like terms:

18x - 4 + 8x + 2 = 180

Combine the x terms:

26x - 2 = 180

Add 2 to both sides of the equation:

26x = 182

Divide both sides by 26:

x = 7

Now we can find the measure of angle A:

Angle A = 9x - 2
Angle A = 9(7) - 2
Angle A = 63 - 2
Angle A = 61

Similarly, we can find the measure of angle B:

Angle B = 8x + 2
Angle B = 8(7) + 2
Angle B = 56 + 2
Angle B = 58

Since ABC is an isosceles triangle, angles A and C have the same measure. Therefore, angle C will also measure 61 degrees.

So, the measure of the three angles in isosceles triangle ABC are:
Angle A = 61 degrees
Angle B = 58 degrees
Angle C = 61 degrees