Question

describing supplementary angle relationships

circle all the problems that show two labeled angles that are supplementary.

then find the value of x for only the circled problems.
1
(4x + 6)°
130°
2
(9x + 36)°
45°
3
(7x - 23)°
140°
4
(15x - 30)°
150°
5
(5x + 25)°
95°
6
(x + 47)°
7x°

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°.

Step2: Solve for problem 1

Set up the equation $130+(4x + 6)=180$.
First, simplify the left - hand side: $130+4x+6 = 136+4x$.
So, $136 + 4x=180$.
Subtract 136 from both sides: $4x=180 - 136=44$.
Divide both sides by 4: $x = 11$.

Step3: Solve for problem 2

Set up the equation $(9x + 36)+45=180$.
Simplify the left - hand side: $9x+36 + 45=9x + 81$.
So, $9x+81 = 180$.
Subtract 81 from both sides: $9x=180 - 81 = 99$.
Divide both sides by 9: $x = 11$.

Step4: Solve for problem 3

Set up the equation $140+(7x - 23)=180$.
Simplify the left - hand side: $140+7x-23=7x + 117$.
So, $7x+117 = 180$.
Subtract 117 from both sides: $7x=180 - 117 = 63$.
Divide both sides by 7: $x = 9$.

Step5: Solve for problem 4

Set up the equation $150+(15x - 30)=180$.
Simplify the left - hand side: $150+15x-30=15x + 120$.
So, $15x+120 = 180$.
Subtract 120 from both sides: $15x=180 - 120 = 60$.
Divide both sides by 15: $x = 4$.

Step6: Solve for problem 5

Set up the equation $95+(5x + 25)=180$.
Simplify the left - hand side: $95+5x+25=5x + 120$.
So, $5x+120 = 180$.
Subtract 120 from both sides: $5x=180 - 120 = 60$.
Divide both sides by 5: $x = 12$.

Step7: Solve for problem 6

Set up the equation $7x+(x + 47)=180$.
Simplify the left - hand side: $7x+x + 47=8x + 47$.
So, $8x+47 = 180$.
Subtract 47 from both sides: $8x=180 - 47 = 133$.
Divide both sides by 8: $x=\frac{133}{8}=16.625$.

Answer:

Problem 1: $x = 11$
Problem 2: $x = 11$
Problem 3: $x = 9$
Problem 4: $x = 4$
Problem 5: $x = 12$
Problem 6: $x = 16.625$