9514 1404 393
Answer:
- consecutive interior angles are supplementary
- x = 19
- Angle A = 116°
Step-by-step explanation:
1. The marked angles are between the parallel lines, so are "interior." They are on the same side of the transversal, so are "consecutive" or "same-side" angles. The relevant relationship is ...
consecutive interior angles are supplementary
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2. Using the above relation, we have ...
A + B = 180
(6x +2) + 64 = 180
6x = 114 . . . . . . . . . . subtract 66
x = 19 . . . . . . . . . . . . divide by 6
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3. Angle B is given. Angle A is the supplement to it. We know it must be ...
A = 180° -64° = 116°
We can check our math by using the given expression for angle A:
A = 6(19) +2 = 114 +2 = 116 . . . . same as above
Angle A is 116°.
