In a `DeltaABC`, AB = BC, `angleB=x^(@)andangleA=(2x-20)^(@)`. Then `angleB` is.
किसी `DeltaABC` में, AB = BC, `angleB=x^(@)` और `angleA=(2x-20^(@))`, तो `angleB` का मान क्या होगा?

Options

A. `54^(@)`
B. `30^(@)`
C. `40^(@)`
D. `44^(@)`

Explanation

To find the value of angle B in triangle ABC where AB = BC, angle B = x degrees, and angle A = (2x - 20) degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Properties of the Triangle**:
Since AB = BC, triangle ABC is an isosceles triangle. This means that the angles opposite to the equal sides are also equal. Therefore, angle A = angle C.

2. **Set Up the Equation for Angles**:
Given:
- Angle A = (2x - 20) degrees
- Angle B = x degrees
- Angle C = angle A = (2x - 20) degrees

3. **Write the Equation for the Sum of Angles in a Triangle**:
The sum of the angles in any triangle is 180 degrees. Thus, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180 \]
Substituting the known values:
\[ (2x - 20) + x + (2x - 20) = 180 \]

4. **Combine Like Terms**:
Simplifying the left side:
\[ 2x - 20 + x + 2x - 20 = 180 \]
This simplifies to:
\[ 5x - 40 = 180 \]

5. **Solve for x**:
Add 40 to both sides:
\[ 5x = 180 + 40 \]
\[ 5x = 220 \]
Now, divide both sides by 5:
\[ x = \frac{220}{5} = 44 \]

6. **Find Angle B**:
Since angle B = x degrees, we have:
\[ \text{Angle B} = 44 \text{ degrees} \]

### Final Answer:
Angle B is 44 degrees.

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