Question

find the range of possible values for x.
the range is <x<.
(simplify your answers.)

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 third side of the first triangle is shorter than the third side of the second triangle, then the included angle of the first triangle is smaller than the included angle of the second triangle.
Here, the two sides of the two triangles are equal (marked with the same tick - marks). The third sides are \(8\) and \(9\) (\(8<9\)). So, \((x - 3)^{\circ}<37^{\circ}\).
Also, since an angle measure must be positive, \((x - 3)^{\circ}>0^{\circ}\).

Step2: Solve the inequalities

For \((x - 3)>0\)

Add \(3\) to both sides of the inequality \(x−3 > 0\).
\(x-3+3>0 + 3\), which gives \(x>3\).

For \(x - 3<37\)

Add \(3\) to both sides of the inequality \(x−3 < 37\).
\(x-3+3<37 + 3\), which gives \(x<40\).

Answer:

\(3