Question

unit 5 review
find the possible values for the value of x.
36
60
33°
(3x - 3)°
30
60
<x<

Explanation:

Step1: Apply the Hinge Theorem

According to the Hinge Theorem, if two sides of one triangle are congruent to two sides of another triangle, then the angle opposite the longer third side is larger.
Here, the two triangles have two sides equal (\(60 = 60\)). The third - side lengths are \(36\) and \(30\). Since \(36>30\), we have the inequality \(33>3x - 3\). Also, for a non - degenerate triangle, the angle \(3x - 3>0\).

Step2: Solve the inequalities

First, solve \(3x−3>0\):
Add \(3\) to both sides of the inequality \(3x−3>0\):
\(3x-3 + 3>0 + 3\), which gives \(3x>3\). Divide both sides by \(3\): \(x > 1\).
Second, solve \(33>3x−3\):
Add \(3\) to both sides: \(33 + 3>3x-3 + 3\), so \(36>3x\). Divide both sides by \(3\): \(x<12\).

Answer:

\(1