Question

In the triangles shown, ABC is dilated by a scale factor of to form XYZ. Given that mA = 45o and mB = 105o, what is mZ?

Answer 1

The value of angle Z is 30 degrees

How to determine the value of angle Z?

The given parameters are:

ABC is dilated to form XYZ

This means that the triangles ABC and XYZ are similar triangles and the corresponding angles are equal

So, we have the following angle equations

A = X

B = Y

C = Z

Also, we have

A + B + C = 180

Substitute C = Z in A + B + C = 180

A + B + Z = 180

Substitute A = 45 and B = 105

So, we have:

45 + 105 + Z = 180

Evaluate the like terms

150 + Z = 180

Subtract 150 from both sides

Z = 30

Hence, the value of angle Z is 30 degrees

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