What is the measure of angle Cin the triangle shown above?
A. 15
B. 30
C. 180
D. 60

D, 60 degrees.

Step-by-step explanation:

They have given you expressions instead of each of the angles. All of the angles inside ANY triangle will always add up to 180 degrees (idk why, it's just a rule of trig).

So first we're just going to find the value of x, since all the expressions are in terms of x. this is how we do it:

1) add up all the expressions and equate it to 180 degrees, because we know that all the angles add up to 180 degrees. this gives us:

2x + 4x + 3x + 45 = 180

2) Keep solving, by adding all the x

9x + 45 = 180

3) Keep solving by moving 45 to the other side

9x = 180 - 45

9x = 135

4) Divide both sides by 9, for x

x = 15

Now that we've found the value of x, we can find C. The diagram tells us that C = 4x.

We know that x is 15 degrees, so C = 4 x 15, which equals 60 degrees.

Hope that helped : )

the circle one