In Hollow Brook Apartments, the roads Harbor and Haven are parallel. Both roads are intersected by Fairway and Parkway.
Picture is not drawn to scale.
What is the measure of angle X?
A.
38°
B.
142°
C.
46°
D.
134°
To find the measure of angle X, we can use the property that when two lines are parallel, alternate interior angles are congruent.
First, we can see that angle Y is congruent to angle X because they are corresponding angles. Therefore, angle Y also measures 46°.
Next, we can see that angle Z is a straight angle, which means it measures 180°.
Now, we can use the fact that the sum of the angles in a triangle is 180° to find angle W.
angle W + angle X + angle Y = 180°
angle W + 46° + 46° = 180°
angle W + 92° = 180°
angle W = 180° - 92°
angle W = 88°
Since angles W and Z are opposite angles, they are congruent. Therefore, angle W also measures 88°.
Finally, we can find angle X by subtracting angles Y and W from angle Z:
angle X = angle Z - angle Y - angle W
angle X = 180° - 46° - 88°
angle X = 46°
Therefore, the measure of angle X is 46°.
The answer is C.