In a `/_\\`ABC, if `/_`A + `/_`B = `65^(@)`  and `/_`B + `/_`C = `140^(@)` . Then, `/_`B = ?

Options

A. `25^(@)`
B. `35^(@)`
C. `40^(@)`
D. `45^(@)`

Answer

To solve the problem step by step, we need to find the value of angle B in triangle ABC given the following conditions:

1. Angle A + Angle B = 65 degrees
2. Angle B + Angle C = 140 degrees

### Step 1: Use the property of triangles
The sum of angles in a triangle is always 180 degrees. Therefore, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]

### Step 2: Substitute the known values
From the first condition, we know:
\[ \text{Angle A} + \text{Angle B} = 65^\circ \]
We can express Angle A in terms of Angle B:
\[ \text{Angle A} = 65^\circ - \text{Angle B} \]

### Step 3: Substitute Angle A in the triangle sum equation
Now, substitute Angle A into the triangle sum equation:
\[ (65^\circ - \text{Angle B}) + \text{Angle B} + \text{Angle C} = 180^\circ \]

### Step 4: Simplify the equation
When we simplify the equation, we get:
\[ 65^\circ + \text{Angle C} = 180^\circ \]

### Step 5: Solve for Angle C
Now, isolate Angle C:
\[ \text{Angle C} = 180^\circ - 65^\circ \]
\[ \text{Angle C} = 115^\circ \]

### Step 6: Use the second condition to find Angle B
Now that we have Angle C, we can use the second condition:
\[ \text{Angle B} + \text{Angle C} = 140^\circ \]
Substituting the value of Angle C:
\[ \text{Angle B} + 115^\circ = 140^\circ \]

### Step 7: Solve for Angle B
Now isolate Angle B:
\[ \text{Angle B} = 140^\circ - 115^\circ \]
\[ \text{Angle B} = 25^\circ \]

### Final Answer
Thus, the value of Angle B is:
\[ \text{Angle B} = 25^\circ \]

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