Question

Find the value of x.
Picture below

Answer 1

The sum of the interior angles of all triangles is 180 degrees. You can set the sum of these interior angle values equal to 180 and solve algebraically to find x.

180 = (4x + 7) + (11x - 9) + 32

Get rid of parentheses.

180 = 4x + 7 + 11x - 9 + 32

Collect like terms.

180 = 15x + 30

Subtract 30 from both sides.

150 = 15x

Divide both sides by 15.

10 = x

To check work, plug in x accordingly and find the sum.

4x + 7

4(10) + 7

40 + 7

47

11x - 9

11(10) - 9

110 - 9

101

47 + 101 + 32 = 180

Answer:

x = 10

Answer 2

All angles in a triangle add up to 180 degrees. Make all the angles in this triangle add up to 180 in an equation to solve for x.

(4x + 7) + (11x - 9) + 32 = 180

Combine like terms. (4x + 11x) and (7 - 9 + 32)

15x + 30 = 180

Subtract 30 from both sides.

15x = 150

Divide both sides by 15.

`\boxed {x = 10}`