Question

Two angles of a triangle have the same measure and the third one is 36 degrees greater than the measure of each of the other two.Find the measure of the LARGEST angle in the triangle.

Answer 1

The angles in a triangle equal 180.
Two angles are the same so they are x + x + (× + 36) = 180 
So, 3x + 36 = 180
Subtract 36 from both sides.  3x = 144
Divide each side by 3      x = 48
The angles are 48, 48, and 48 + 36= 84
The largest angle is 84.

Answer 2

All the angles of a triangle add up to 180 degrees.
Since two of the angles are the same, we can write:

2A+B=180

Where 2A accounts for the two angles that are the same.
We are given the relation:

B=A+30

We can plug this into our first equation:

2A+A+30=180


Combine like terms and move the 30 to the other side:

3A=150

Divide both sides by 3:

A=50

We can solve for B by plugging A back into our relation:

B=50+30
B=80 
To check: 80+50+50 so we are correct.