Answer:
8. x=6; supplementary consecutive interior angles
10. x = 4; no applicable theorem
Step-by-step explanation:
8.
The marked angles are "consecutive interior" angles. When their sum is 180°, the lines l and m will be parallel.
(7x -15) +(24x +9) = 180
31x = 186
x = 6
Consecutive interior angles being supplementary will make the lines parallel.
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10.
The sum of the remote interior angles of a triangle is equal to the exterior angle:
28x = 48 +16x
12x = 48
x = 4
The above relation holds regardless of whether line l is parallel to line m. There is no applicable theorem or converse.
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Additional comment
Adding the marking shown in the attachment would make the converse of the alternate interior angles theorem applicable to problem 10.
