In a `Delta ABC , angle A + angle B = 118^@`
`angle A + angle C = 96^@` . Find the value of `angle A`

Options

A. `36^@`
B. `40^@`
C. `30^@`
D. `34^@`

Answer

To find the value of angle A 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. \( \angle A + \angle B = 118^\circ \) (Equation 1)
2. \( \angle A + \angle C = 96^\circ \) (Equation 2)

### Step 2: Use the property of triangles.
The sum of the angles in a triangle is always \( 180^\circ \):
\[ \angle A + \angle B + \angle C = 180^\circ \quad (Equation 3) \]

### Step 3: Substitute Equation 1 into Equation 3.
From Equation 1, we can express \( \angle C \):
\[ \angle C = 180^\circ - (\angle A + \angle B) = 180^\circ - 118^\circ = 62^\circ \]

### Step 4: Substitute the value of \( \angle C \) into Equation 2.
Now we substitute \( \angle C \) into Equation 2:
\[ \angle A + 62^\circ = 96^\circ \]

### Step 5: Solve for \( \angle A \).
Now, we can solve for \( \angle A \):
\[ \angle A = 96^\circ - 62^\circ = 34^\circ \]

### Conclusion:
Thus, the value of \( \angle A \) is \( 34^\circ \).

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