z = 5
m∠MNP = 34°
Solution:
Given data:
∠MNV = (2z + 10)°
∠VNP = (4z – 6)°
In angle MNP,
m∠MNV ≅ m∠VNP
⇒ (2z + 10)° = (4z – 6)°
⇒ 2z° + 10° = 4z° – 6°
Add 6° on both sides of the equation.
⇒ 2z° + 16° = 4z°
Subtract 2z° on both sides of the equation.
⇒ 10° = 2z°
Switch the sides of the equation.
⇒ 2z° = 10°
Divide by 2 on both sides of the equation.
⇒ z° = 5°
⇒ z = 5
m∠MNP = m∠MNV + m∠VNP
= (2z + 10)° + (4z – 6)°
= (2 (5) + 10)° + (4(5) – 6)°
= (10 + 10)° + (20 – 6)°
= 20° + 14°
m∠MNP = 34°
