In `triangle ABC` ,` AB = AC` , `angle B = 40 ^(@)` Then `angle C` is equal to

Options

A. `50^(@)`
B. `40^(@)`
C. `80^(@)`
D. `140^(@)`

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the properties of the triangle
We are given triangle ABC where AB = AC. This indicates that triangle ABC is an isosceles triangle.

**Hint:** Remember that in an isosceles triangle, the angles opposite the equal sides are also equal.

### Step 2: Use the given information
We know that angle B = 40 degrees. Since AB = AC, the angles opposite these sides (angle B and angle C) must be equal.

**Hint:** Look for relationships between the angles when sides are equal in a triangle.

### Step 3: Set up the equation for the angles
Since angle B = angle C in this isosceles triangle, we can write:
- angle C = angle B = 40 degrees.

**Hint:** When two angles are equal, you can substitute one for the other.

### Step 4: Conclude the solution
Thus, angle C is also equal to 40 degrees.

**Final Answer:** Angle C = 40 degrees.

### Summary of Steps:
1. Identify that triangle ABC is isosceles (AB = AC).
2. Use the property that angles opposite equal sides are equal.
3. Set angle C equal to angle B.
4. Conclude that angle C = 40 degrees.