Two supplementary angles are ∠ABC=135° and ∠CBD=9x°. What is the equation to solve for x?
A: 9x−135=180
B: 9x+135=90
C: 9x+135=180
D: 9x=180
−135
Answer: C: 9x+135=180
To solve for x, we need to use the fact that supplementary angles add up to 180 degrees.
We are given that ∠ABC is 135 degrees and ∠CBD is 9x degrees. Since ∠ABC and ∠CBD are supplementary, their measures add up to 180 degrees.
So we can set up the equation as follows:
∠ABC + ∠CBD = 180
135 + 9x = 180
To isolate the term with x, we can subtract 135 from both sides:
135 + 9x - 135 = 180 - 135
9x = 45
Now we can divide both sides by 9 to solve for x:
9x/9 = 45/9
x = 5
Therefore, the correct equation to solve for x is:
9x + 135 = 180
So the answer is option C: 9x + 135 = 180.
The sum of two supplementary angles is 180 degrees. To find the equation to solve for x, we can set up the following equation:
∠ABC + ∠CBD = 180
Substituting the given angles:
135 + 9x = 180
Now, we can solve for x:
135 + 9x - 135 = 180 - 135
9x = 45
Dividing both sides by 9:
x = 5
So, the equation to solve for x is 9x + 135 = 180. Therefore, the correct option is C: 9x + 135 = 180.