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