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. The angle made between the diagonal support bar and horizontal bar 1 is 47°. What is the measure of angle X?
To find the measure of angle X, we need to find the measure of angle Y first.
Since the diagonal support bar intersects horizontal bar 1 at a right angle, angle Y is also 90°.
Therefore, the measure of angle X is:
180° - angle Y - angle made between diagonal support bar and horizontal bar 1
= 180° - 90° - 47°
= 180° - 137°
= 43°
So, the measure of angle X is 43°.
To find the measure of angle X, we need to gather the information given in the problem and use geometric properties and relationships.
Let's label the various components of the fence gate:
- Vertical posts: Let's number them from left to right as post 1, post 2, post 3, post 4, post 5, post 6, and post 7.
- Horizontal bars: Let's name them as horizontal bar 1 (top) and horizontal bar 2 (bottom).
- Diagonal support bar: Let's call it diagonal bar.
According to the problem, the angle between the diagonal support bar and horizontal bar 1 is 47°. Let's denote this angle as angle A.
Now, let's start by drawing a diagram of the fence gate:
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Let's use this diagram to find the measure of angle X step by step:
Step 1: Identify the right triangle formed by the diagonal bar, horizontal bar 1, and a vertical post.
The right triangle is formed by the diagonal bar, horizontal bar 1, and the vertical post that the diagonal bar and horizontal bar 1 intersect at. In our diagram, let's label this vertical post as post 4.
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/Θ |
post 4 horizontal bar 1 diagonal bar
Step 2: Determine the angle Θ.
Since we know that angle A (the angle between the diagonal bar and horizontal bar 1) is 47°, we can use the fact that opposite angles in a parallelogram are equal. This means that angle Θ is also 47°.
Step 3: Determine the measure of angle X.
Angle X is the complementary angle to angle Θ. Complementary angles add up to 90°. Therefore, angle X = 90° - angle Θ.
Substituting the value of angle Θ (47°), we have:
angle X = 90° - 47°
angle X = 43°
Therefore, the measure of angle X is 43°.
In summary, the measure of angle X in the given fence gate is 43°.
To find the measure of angle X, we need to determine the angle between the diagonal support bar and horizontal bar 2.
Since the vertical posts are parallel and the diagonal support bar intersects horizontal bar 1, it forms alternate interior angles with the vertical posts. Therefore, the angle between the diagonal support bar and horizontal bar 1 is also the angle between the diagonal support bar and horizontal bar 2.
So, the measure of angle X is also 47°.