Answer:
a) x = 21
b) 136º
Step-by-step explanation:
The sum of all the angle measures within a triangle is equal to 180º. Therefore, we can use an equation to find x and find the measure of angle C.
x + 6x + 10 + x + 2 = 180
Let's add together all the x's.
8x + 10 + 2 = 180
Now let's add together 10 + 2.
8x + 12 = 180.
To solve for x, we must first isolate 8x. To do this, we subtract 12 from both sides.
8x + 12 - 12 = 180 - 12.
8x = 168
To solve for x, we must divide 8 from both sides.
8x / 8 = 168 / 8
x = 21
Now we have the answer to the first part.
We can use this answer to solve for the measure of angle C.
Angle C = 6x + 10.
We just have to plug in 21 for x and solve for angle C.
6(21) + 10 = 136.
Angle C has a measure of 136º.
