Three angles have measures that add to 180°. They have the following angle measures: m ABC = (×-6)°, m CBD = (4×-14)°, and m DBE = 5x°. What is the equation to solve for x?
A. 10x° + 20° = 180°
B. 10x° - 20° =180
C. 9x°-20°=180°
D. x°-20°=180°
To find the equation to solve for x, we can set up the equation by adding the angle measures and setting the sum equal to 180°.
m ABC + m CBD + m DBE = 180°
Using the given angle measures, we have:
(×-6)° + (4×-14)° + 5x° = 180°
Simplifying the equation:
× - 6 + 4× - 14 + 5x = 180
Combining like terms:
10× - 20 + 5x = 180
Thus, the equation to solve for x is:
10x° + 5x° - 20° = 180°
Which is equivalent to:
10x° + 5x° = 180° + 20°
Simplifying further:
15x° = 200°
Therefore, the equation to solve for x is:
15x° = 200°
So, option D. x° - 20° = 180° is the correct equation to solve for x.