Question

1. (10 pts) solve for \\(x\\) and find \\(m\angle cat\\)

Explanation:

Set up the angle sum equation

The sum of angles in a triangle is \(180^\circ\).
Using the Triangle Angle Sum Theorem, we write:

$$(x + 37) + (x + 67) + 90 = 180$$

Solve for x

Using the Linear Equation Solving knowledge point:

$$
LATEXBLOCK0
$$

Find the measure of angle CAT

The angle \(m\angle CAT\) is represented by \(x + 37\).
Substitute \(x = -7\):

$$m\angle CAT = -7 + 37 = 30^\circ$$

Answer:

\(x = -7\), \(m\angle CAT = 30^\circ\)