In a `Delta ABC, angleA = 90^@, angle C =55^@ and AD _|_BC`. What is the value of `angle BAD`?

Options

A. `60^@`
B. `45^@`
C. `55^@`
D. `35^@`

Answer

To find the value of angle BAD in triangle ABC where angle A = 90°, angle C = 55°, and AD is perpendicular to BC, we can follow these steps:

### Step 1: Determine angle B
In any triangle, the sum of the angles is always 180°. Given that angle A = 90° and angle C = 55°, we can find angle B as follows:

\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180° \]

Substituting the known values:

\[ 90° + \text{Angle B} + 55° = 180° \]

Now, combine the known angles:

\[ 145° + \text{Angle B} = 180° \]

Now, solve for angle B:

\[ \text{Angle B} = 180° - 145° = 35° \]

### Step 2: Analyze triangle ADB
Now, we will focus on triangle ADB. In triangle ADB, we know:

- Angle ADB = 90° (since AD is perpendicular to BC)
- Angle BAD = ? (this is what we are trying to find)
- Angle ABD = Angle B = 35° (from Step 1)

### Step 3: Use the angle sum property in triangle ADB
The sum of angles in triangle ADB is also 180°:

\[ \text{Angle ADB} + \text{Angle BAD} + \text{Angle ABD} = 180° \]

Substituting the known values:

\[ 90° + \text{Angle BAD} + 35° = 180° \]

### Step 4: Solve for angle BAD
Now, combine the known angles:

\[ 125° + \text{Angle BAD} = 180° \]

Now, solve for angle BAD:

\[ \text{Angle BAD} = 180° - 125° = 55° \]

### Conclusion
Thus, the value of angle BAD is:

\[ \text{Angle BAD} = 55° \]

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