Question

Find the measure of /_ MFZ

Answer 1

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.