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

1 answer

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.