In `Delta ABC, /_B = 60^@, /_C = 40^@, AD `is the bisector of `/_A and AE` is drawn perpendicular on BC from A. Then the measure of `/_EAD `IS

Options

A. `40^@`
B. `30^@`
C. `10^@`
D. `80^@`

Answer

To solve the problem, we need to find the measure of angle EAD in triangle ABC, where AD is the bisector of angle A and AE is perpendicular to BC.

### Step-by-Step Solution:

1. **Identify the Angles in Triangle ABC:**
- Given: Angle B = 60° and Angle C = 40°.
- To find Angle A, we use the property that the sum of angles in a triangle is 180°.
\[ \text{Angle A} = 180° - \text{Angle B} - \text{Angle C} = 180° - 60° - 40° = 80° \]

**Hint:** Remember that the sum of the angles in a triangle is always 180°.

2. **Use the Angle Bisector Theorem:**
- Since AD is the bisector of angle A, it divides angle A into two equal parts.
\[ \text{Angle BAD} = \text{Angle CAD} = \frac{1}{2} \times \text{Angle A} = \frac{1}{2} \times 80° = 40° \]

**Hint:** The angle bisector divides the angle into two equal parts.

3. **Analyze Triangle ABE:**
- Since AE is perpendicular to BC, we have a right triangle ABE.
- In triangle ABE, we know:
- Angle ABE = Angle B = 60°
- Angle BAD = 40° (from the previous step)
- Therefore, we can find angle EAD:
\[ \text{Angle EAD} = \text{Angle BAD} - \text{Angle ABE} = 40° - 60° = -20° \text{ (which is not possible)} \]
- This means we should consider the correct angles in triangle ABE.

4. **Calculate Angle EAD:**
- We can use the relation involving the angle bisector and the right angle:
\[ \text{Angle EAD} = \frac{1}{2} \times (\text{Angle B} - \text{Angle C}) = \frac{1}{2} \times (60° - 40°) = \frac{1}{2} \times 20° = 10° \]

**Hint:** The angle EAD can be calculated using the difference of angles divided by 2 when perpendiculars and angle bisectors are involved.

### Final Answer:
The measure of angle EAD is **10°**.