`DeltaABC~=DeltaXYZ,angleA=50^(@),angleB=60^(@)` then measure of `angleZ` is

Options

A. `50^(@)`
B. `60^(@)`
C. `70^(@)`
D. can't be determined

Answer

To find the measure of angle Z in triangle XYZ, given that triangle ABC is congruent to triangle XYZ, and that angle A = 50° and angle B = 60°, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Congruence**: Since triangle ABC is congruent to triangle XYZ (ΔABC ≅ ΔXYZ), the corresponding angles of the triangles are equal. This means:
- Angle A = Angle X
- Angle B = Angle Y
- Angle C = Angle Z

2. **Assign Given Values**: We know from the problem:
- Angle A = 50°
- Angle B = 60°

3. **Find Corresponding Angles**: Using the congruence property:
- Since Angle A = Angle X, we have:
- Angle X = 50°
- Since Angle B = Angle Y, we have:
- Angle Y = 60°

4. **Use Angle Sum Property**: The sum of the angles in any triangle is 180°. Therefore, for triangle ABC:
- Angle A + Angle B + Angle C = 180°
- Substituting the known values:
- 50° + 60° + Angle C = 180°

5. **Calculate Angle C**: Now, we can solve for Angle C:
- 50° + 60° = 110°
- Thus, Angle C = 180° - 110° = 70°

6. **Find Angle Z**: Since Angle C = Angle Z (by CPCT), we conclude:
- Angle Z = 70°

### Final Answer:
The measure of angle Z is **70°**.