In a `/_\`ABC, /_`A - `/_`B = `33^(@)`  and `/_`B-`/_`C = `18^(@)` . Then, `/_`B = ?

Options

A. `35^(@)`
B. `55^(@)`
C. `45^(@)`
D. `57^(@)`

Answer

To find the value of angle B in triangle ABC, we can follow these steps:

### Step 1: Set up the equations based on the given information.
We are given two equations:
1. \( \angle A - \angle B = 33^\circ \)
2. \( \angle B - \angle C = 18^\circ \)

### Step 2: Express angle A and angle C in terms of angle B.
From the first equation:
\[ \angle A = \angle B + 33^\circ \]

From the second equation:
\[ \angle C = \angle B - 18^\circ \]

### Step 3: Use the triangle angle sum property.
The sum of the angles in a triangle is \( 180^\circ \):
\[ \angle A + \angle B + \angle C = 180^\circ \]

Substituting the expressions for angle A and angle C:
\[ (\angle B + 33^\circ) + \angle B + (\angle B - 18^\circ) = 180^\circ \]

### Step 4: Simplify the equation.
Combine like terms:
\[ \angle B + 33^\circ + \angle B + \angle B - 18^\circ = 180^\circ \]
\[ 3\angle B + 15^\circ = 180^\circ \]

### Step 5: Isolate angle B.
Subtract \( 15^\circ \) from both sides:
\[ 3\angle B = 180^\circ - 15^\circ \]
\[ 3\angle B = 165^\circ \]

Now, divide by 3:
\[ \angle B = \frac{165^\circ}{3} \]
\[ \angle B = 55^\circ \]

### Final Answer:
Thus, the value of \( \angle B \) is \( 55^\circ \).

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