Given:
[tex]MZ\cong PZ[/tex]
[tex]m\angle MFZ=(x+9)^\circ[/tex]
[tex]m\angle PFZ=(2x-1)^\circ[/tex]
To find:
The measure of angle MFZ.
Solution:
In triangles MFZ and PFZ,
[tex]m\angle FMZ\cong \angle FPZ[/tex] (Right angle)
[tex]MZ\cong PZ[/tex] (Given)
[tex]FZ\cong FZ[/tex] (Common side)
[tex]\Delta MFZ\cong \Delta PFZ[/tex] (HL congruent postulate)
[tex]\angle MFZ\cong \angle PFZ[/tex] (CPCTC)
[tex]m\angle MFZ=m\angle PFZ[/tex]
[tex]x+9=2x-1[/tex]
[tex]9+1=2x-x[/tex]
[tex]10=x[/tex]
The value of x is 10.
The measure of angle MFZ is:
[tex]m\angle MFZ=(x+9)^\circ[/tex]
[tex]m\angle MFZ=(10+9)^\circ[/tex]
[tex]m\angle MFZ=19^\circ[/tex]
Therefore, the measure of angle MFZ is 19 degrees.
