1 Answer

Eyk Rehbein · Answer 1 · 2022-01-17T19:30:41+0000

Given:

$MZ\cong PZ$

$m\angle MFZ=(x+9)^\circ$

$m\angle PFZ=(2x-1)^\circ$

To find:

The measure of angle MFZ.

Solution:

In triangles MFZ and PFZ,

$m\angle FMZ\cong \angle FPZ$ (Right angle)

$MZ\cong PZ$ (Given)

$FZ\cong FZ$ (Common side)

$\Delta MFZ\cong \Delta PFZ$ (HL congruent postulate)

$\angle MFZ\cong \angle PFZ$ (CPCTC)

$m\angle MFZ=m\angle PFZ$

x+9=2x-1

9+1=2x-x

10=x

The value of x is 10.

The measure of angle MFZ is:

$m\angle MFZ=(x+9)^\circ$

$m\angle MFZ=(10+9)^\circ$

$m\angle MFZ=19^\circ$

Therefore, the measure of angle MFZ is 19 degrees.

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