Answer:
Explanation:
Given a transversal crossing parallel lines and supplementary angles (x+8°) and (2x-5°), you want to find the measures of angles L and O, supplementary to each of these.
Consecutive interior angles
Where a transversal crosses parallel lines, consecutive interior angles are supplementary. Using the given expressions, this means ...
(x +8°) +(2x -5°) = 180°
3x +3° = 180° . . . . . . . . . simplify
x +1° = 60° . . . . . . . divide by 3
x = 59° . . . . . . subtract 1°
Then the acute angle is ...
x+8° = 59° +8° = 67°
and the obtuse angle is ...
2x -5° = 2(59°) -5° = 113°
Relation to other angles
Angle L corresponds to angle (2x-5°), so is congruent:
∠L = 113°
Angle O is an alternate interior angle with respect to angle (x+8°), so is congruent:
∠O = 67°