t is the interior of angle car, measure car = 80 degrees and the measure of cat is 10 more than the measure of angle tar.

Question

sketch the situation and find the measure of cat and the measure of tar

Answer 1

I can't sketch this for you, but essentially you draw any angle CAR. Somewhere inside of CAR, draw point T. Connect point T to point A with a line. Now you have 3 total angles, CAR, CAT and TAR. CAR is the biggest angle with CAT and TAR inside of it. 

 

Let measure angle TAR = x. You know the measure of angle CAT is 10 more than TAR, so let measure of angle CAT = x+10.

 

Looking at your sketch, you should see that measure of angle CAT + measure of angle TAR = measure of angle CAR. If we write this out using algebra:

 

(x+10) + x = 80

 

Solving for x:

 

2x +10 = 80

2x = 70

x= 35

 

Plug 35 back into your equations to get the angles measures: TAR = 35 degrees, and CAT = (35+10) = 45 degrees.

 

You can check if you're right, because TAR + CAT = 80, and 35 + 45 does indeed = 80 degrees.