ABCD is a parallelogram and BD is a diagonal. `angleBAD = 65^(@)` and `angleDBC = 45^(@)`, then m `angleBDC` is :

Options

A. `65^(@)`
B. `70^(@)`
C. `20^(@)`
D. none of these

Answer

To solve the problem, we need to find the measure of angle BDC in the parallelogram ABCD, given that angle BAD = 65° and angle DBC = 45°.

### Step-by-Step Solution:

1. **Identify the Angles in the Parallelogram:**
- Given that ABCD is a parallelogram, we know that opposite angles are equal. Therefore, angle DAB (which is the same as angle BAD) is equal to angle DCB.
- Thus, angle DCB = angle BAD = 65°.

2. **Use the Triangle Sum Property:**
- In triangle DBC, we have the angles DBC, BDC, and BCD. The sum of the angles in any triangle is 180°.
- Therefore, we can write the equation:
\[ \text{angle DBC} + \text{angle BDC} + \text{angle BCD} = 180° \]

3. **Substitute the Known Values:**
- We know that angle DBC = 45° and angle BCD = 65° (from step 1).
- Substituting these values into the equation gives:
\[ 45° + \text{angle BDC} + 65° = 180° \]

4. **Simplify the Equation:**
- Combine the known angles:
\[ 110° + \text{angle BDC} = 180° \]

5. **Solve for Angle BDC:**
- To find angle BDC, subtract 110° from both sides:
\[ \text{angle BDC} = 180° - 110° = 70° \]

### Final Answer:
- Therefore, the measure of angle BDC is **70°**.

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