Question

write an inequality describing the range of x for each pair of triangles.
a. b.
a x < (simplify your answer.)

Explanation:

Step1: Apply the Hinge Theorem

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.
For part a, we have two sides congruent in both triangles. Since \(41>32\), we can set up the inequality \(75 < 5x - 60\).

Step2: Solve the inequality

Add \(60\) to both sides of the inequality \(75 < 5x - 60\):
\(75+60<5x - 60+60\)
\(135 < 5x\)
Divide both sides by \(5\):
\(\frac{135}{5}<\frac{5x}{5}\)
\(27 < x\)

Answer:

\(x>27\)