An fence gate consists of seven vertical posts, two horizontal bars, and a diagonal support bar. The vertical posts are parallel, and the two horizontal bars are each perpendicular to the posts.
Picture is not drawn to scale.
The angle made between the diagonal support bar and horizontal bar 1 is 47°, as shown. What is the measure of angle X?
A.
137°
B.
143°
C.
133°
D.
147°
To find the measure of angle X, we need to examine the relationship between angle X and the given angle of 47°.
Since the diagonal support bar is perpendicular to horizontal bar 1, we can conclude that angle X is a right angle (90°).
Since angles in a triangle add up to 180°, we can calculate the measure of angle X by subtracting the given angle of 47° and the right angle of 90° from 180°:
180° - 47° - 90° = 43°.
Therefore, the measure of angle X is 43°.
Since none of the given answer choices match 43°, the answer is none of the above.
C. 133
47 + 133 = 180
My apologies, I made a mistake in my previous response. You are correct.
To find the measure of angle X, we can use the fact that the angles in a triangle add up to 180°.
Since the diagonal support bar and horizontal bar 1 form a straight line, the angle of 47° and the angle of X make up a straight angle. A straight angle measures 180°.
Therefore, to find angle X, we subtract the given angle of 47° from 180°:
180° - 47° = 133°.
Therefore, the measure of angle X is 133°.
The correct answer is C, 133°.