Mark against the correct answer:
One of the base angles of an isosceles triangle is `70^(@)` The vertical angle is

Options

A. `60^(@)`
B. `80^(@)`
C. `40^(@)`
D. `35^(@)`

Answer

To solve the problem step by step, we need to find the vertical angle (angle A) of an isosceles triangle where one of the base angles (angle B) is given as 70 degrees.

### Step-by-Step Solution:

1. **Identify the properties of the isosceles triangle**:
In an isosceles triangle, two sides are equal, and the angles opposite those sides are also equal.

2. **Assign the angles**:
Let’s denote the angles of triangle ABC as follows:
- Angle A (the vertical angle)
- Angle B (one of the base angles)
- Angle C (the other base angle)

Given that angle B = 70 degrees, and since it is an isosceles triangle, angle C will also be 70 degrees.

3. **Use the triangle angle sum property**:
The sum of all angles in a triangle is always 180 degrees. Therefore, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]

4. **Substitute the known values**:
Substitute the known values into the equation:
\[ \text{Angle A} + 70^\circ + 70^\circ = 180^\circ \]

5. **Simplify the equation**:
Combine the angles:
\[ \text{Angle A} + 140^\circ = 180^\circ \]

6. **Isolate angle A**:
To find angle A, subtract 140 degrees from both sides:
\[ \text{Angle A} = 180^\circ - 140^\circ \]

7. **Calculate angle A**:
\[ \text{Angle A} = 40^\circ \]

Thus, the vertical angle (angle A) is 40 degrees.

### Final Answer:
The vertical angle is **40 degrees**.

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