Three supplementary angles are ∠ABC=(x−6)°, ∠CBD=(4x−14)°, and ∠DBE=5x°. What is the equation to solve for x?
A: x−20=180
B: 10x−20=180
C: 10x+20=180
D: 9x−20=180
B: 10x−20=180
To solve for x, we need to set up an equation using the fact that the sum of the measures of supplementary angles is 180 degrees.
The given angles are ∠ABC, ∠CBD, and ∠DBE. We know that these angles are supplementary, which means their measures add up to 180 degrees.
So, the equation we can set up is:
∠ABC + ∠CBD + ∠DBE = 180
Substituting the given expressions for the angles:
(x - 6) + (4x - 14) + 5x = 180
Now we can simplify and solve for x:
Combine like terms:
x + 4x + 5x - 6 - 14 = 180
10x - 20 = 180
Thus, the equation to solve for x is 10x - 20 = 180.
Therefore, the correct answer is option D: 9x - 20 = 180.
To find the equation to solve for x, we need to set up an equation using the property that the sum of supplementary angles is 180 degrees.
The given angles are ∠ABC = (x-6)°, ∠CBD = (4x-14)°, and ∠DBE = 5x°.
According to the property of supplementary angles, we have:
∠ABC + ∠CBD + ∠DBE = 180
Substituting in the given values, we get:
(x-6) + (4x-14) + 5x = 180
Simplifying the equation, we combine like terms:
10x - 20 = 180
Therefore, the correct equation to solve for x is:
10x - 20 = 180
Thus, the answer is option D: 9x - 20 = 180.