Question

Find the range of possible values for x.

Answer 1

First it must be positive

• 4x-20>0
• 4(x-5)>0
• x-5>0
• x>5

And

• 4x-20<112
• 4x<132
• x<33

So solution range

• (5,33)

Answer 2

• x is between 5 and 33 ⇒ 5 < x < 33

Explanation:

The two triangles have two equal side measures:

• 4 units and the sides marked as equal,

The third side is different and the given angles are opposite them.

It means the angle measure 4x - 20 is smaller than 112:

• 4x - 20 < 112
• 4x < 132
• x < 132/4
• x < 33

On the other hand, the angle measure is positive:

• 4x - 20 > 0
• 4x > 20
• x > 5

So the possible range of x is:

• 5 < x < 33