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

Answer 1

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.