m∠Z = 55°
Solution:
Given m∠A = 75° and m∠B = 50°
Let us first find the m∠C.
Sum of the angles of the triangle is 180°.
In ΔABC,
m∠A + m∠B + m∠C = 180°
⇒ 75° + 50° + m∠C = 180°
⇒ 125° + m∠C = 180°
⇒ m∠C = 180° – 125°
⇒ m∠C = 55°
Given ΔABC ≅ ΔXYZ.
Corresponding parts of congruence triangles are congruent.
⇒ m∠Z = m∠C
⇒ m∠Z = 55°
Hence, m∠Z = 55°.
