9514 1404 393
Answer:
x = 20°
Step-by-step explanation:
Assuming parallel lines, the two angles marked with measures are complementary to each other.
45° +(5x +35°) = 180°
5x = 100° . . . . . . . . . . . . subtract 80° from both sides
x = 20° . . . . . . . . divide by 5
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<em>Comment on the geometry</em>
Where a transversal crosses parallel lines, all of the obtuse angles are congruent, and all of the acute angles are congruent. Of course, the acute angles and obtuse angles are linear pairs, hence supplementary. (The only time this won't apply is when all angles are right angles.)
No lines are marked as parallel here, nor does any part of this problem statement say there are parallel lines. So, we cannot find the value of x if we're going strictly by what is shown in the diagram. In the absence of any information, we can only say that the angle marked with an x-expression must be between 0° and 180°.
0 ≤ 5x +35 ≤ 180 ... -35 ≤ 5x ≤ 145 ... -7 ≤ x ≤ 29.
