In an isosceles triangle `DeltaABC`, if ` angle B=70^(@) ` find `angleA`

Options

A. `40^(@)`
B. `70^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

To find angle A in the isosceles triangle ΔABC where angle B is given as 70 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of Isosceles Triangle**:
In an isosceles triangle, two sides are equal, and the angles opposite those sides are also equal. In triangle ΔABC, since it is isosceles, we can say that if AB = AC, then angle B = angle C.

2. **Identify Given Information**:
We are given that angle B = 70 degrees. Since angle B and angle C are equal, we can conclude that:
\[ \text{angle C} = \text{angle B} = 70^\circ \]

3. **Use the Angle Sum Property of a Triangle**:
The sum of the angles in any 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**:
Now, substituting the known values into the equation:
\[ \text{angle A} + 70^\circ + 70^\circ = 180^\circ \]

5. **Simplify the Equation**:
Combine the angles B and C:
\[ \text{angle A} + 140^\circ = 180^\circ \]

6. **Solve for Angle A**:
To find angle A, subtract 140 degrees from both sides:
\[ \text{angle A} = 180^\circ - 140^\circ \]
\[ \text{angle A} = 40^\circ \]

### Final Answer:
Thus, angle A is 40 degrees.

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