Question

Identify the range of values for x . The figure shows two triangles S P V and S T V. Side P V is congruent to side T V. Angle P V S measures 3 times x plus 9 degrees. Side S P has a length of 19 units. Angle T V S is a right angle. Side S T has a length of 20 units. 3 < x < 27 −3 < x < 27 10 < x < 11 19 < x < 20

Answer 1

To identify the range of values for x, let's analyze the given information:

1. Side SP has a length of 19 units.

2. Side ST has a length of 20 units.

3. Angle PVS measures 3 times x plus 9 degrees.

4. Angle TVS is a right angle.

To find the range of values for x, we need to consider the properties of triangles and angle measurements.

Since side PV is congruent to side TV and angle TVS is a right angle, we can conclude that triangles SPV and STV are similar triangles. This means that the corresponding angles in these triangles are congruent.

Angle PVS corresponds to angle TVS in the similar triangles. Since angle TVS is a right angle, we know that angle PVS must also be a right angle.

To find the range of values for x, we need to determine the possible values that make angle PVS a right angle.

Given that angle PVS measures 3 times x plus 9 degrees, we can set up the following inequality:

3x + 9 = 90

Now, let's solve for x:

3x = 90 - 9

3x = 81

x = 27

Therefore, the range of values for x is 27. In other words, x can only be 27.

To summarize, the correct answer is:

x = 27

Explanation: