1) Two angles of a triangle measure x + 9 and 2x - 7. What is the measure of the third angle as a

simplified expression in terms of x?

178 - 3x.

Step-by-step explanation:

The three angles in a triangle add up to 180 degrees so an expression for the third angle is:

180 - (x + 9) - (2x - 7)

Distributing the negative over the parentheses, we have

180 - x - 9 - 2x + 7

= 180 - 9 + 7 - x - 2x

= 180 - 2 - 3x

= 178 - 3x (answer).

178-3x

Step-by-step explanation:

The three angles of a triangle add to 180 degrees

<1 + <2 + <3 = 180

Let angle 1 = x+9 and <2 = 2x-7

x+9 + 2x-7 + <3 = 180

Combine like terms

3x+2 + <3 = 180

Subtract 3x from each side

3x-3x+2 + <3 = 180-3x

2+<3 = 180-3x

Subtract 2 from each side

2-2 + <3 = 180-2-3x

<3 = 178 - 3x