In `/_\ABC,AB=AC` and`/_B=65^(@)` then `/_C` is equal to

Options

A. `130^(@)`
B. `32^(@)`
C. `70^(@)`
D. `65^(@)`

Answer

To solve the problem step by step, we will use the properties of an isosceles triangle.

### Step 1: Identify the triangle type
We are given triangle ABC where AB = AC. This means triangle ABC is an isosceles triangle.

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

### Step 2: Use the given angle
We are given that angle B = 65 degrees.

**Hint:** Keep in mind that the angles in a triangle always sum up to 180 degrees.

### Step 3: Set up the equation for the angles
In triangle ABC, since AB = AC, the angles opposite these sides (angle B and angle C) are equal. Therefore, we can say:
- Angle B = Angle C

Since angle B is given as 65 degrees, we can write:
- Angle C = 65 degrees

**Hint:** Use the property of isosceles triangles that states angles opposite equal sides are equal.

### Step 4: Conclusion
Thus, angle C is also 65 degrees.

**Final Answer:** Angle C = 65 degrees.