Question
Use the image to answer the question. Find angle x . Show your work. (1 point) Responses 158° 158 degrees 68° 68 degrees 90° 90 degrees 22° 22 degrees Skip to navigation the bottem right is missing and the numbers are 112 degrees in the top left and in the bottem left is 90 degrees
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Answered by
GPT-4o mini
To find angle \( x \), we can use the properties of angles in a triangle and the sum of angles in a linear pair.
Given:
- The triangle has one angle of \( 112^\circ \) at the top left.
- The bottom left angle is \( 90^\circ \).
1. **Determine the third angle in the triangle.** In any triangle, the sum of all angles is \( 180^\circ \).
\[
\text{Third angle} = 180^\circ - (112^\circ + 90^\circ)
\]
\[
\text{Third angle} = 180^\circ - 202^\circ = -22^\circ
\]
However, this result implies that \( 112^\circ + 90^\circ \) represents an external angle adjacent to \( x \). Let's analyze it with respect to a straight line (linear pair).
2. **Consider the angles on the bottom right corner.** Since we know it's adjacent to \( x \) (let's denote it as angle \( a \), which is what we are looking for), we can use:
\[
a + 112^\circ = 180^\circ
\]
solving for \( a \):
\[
a = 180^\circ - 112^\circ = 68^\circ
\]
Thus, angle \( x = 68^\circ \).
The answer is:
\[
\text{Angle } x = 68^\circ
\]
Therefore, the correct response is:
68° or 68 degrees.
Given:
- The triangle has one angle of \( 112^\circ \) at the top left.
- The bottom left angle is \( 90^\circ \).
1. **Determine the third angle in the triangle.** In any triangle, the sum of all angles is \( 180^\circ \).
\[
\text{Third angle} = 180^\circ - (112^\circ + 90^\circ)
\]
\[
\text{Third angle} = 180^\circ - 202^\circ = -22^\circ
\]
However, this result implies that \( 112^\circ + 90^\circ \) represents an external angle adjacent to \( x \). Let's analyze it with respect to a straight line (linear pair).
2. **Consider the angles on the bottom right corner.** Since we know it's adjacent to \( x \) (let's denote it as angle \( a \), which is what we are looking for), we can use:
\[
a + 112^\circ = 180^\circ
\]
solving for \( a \):
\[
a = 180^\circ - 112^\circ = 68^\circ
\]
Thus, angle \( x = 68^\circ \).
The answer is:
\[
\text{Angle } x = 68^\circ
\]
Therefore, the correct response is:
68° or 68 degrees.
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