ABCD is a rhombus in which ∠ADB = 25°. Then, the value of (2∠BAD − ∠ABC) is:

Solution

Given: ABCD is a rhombus and ∠ADB = 25°.

Properties of a Rhombus:

• Diagonals bisect the vertex angles.

• Opposite angles are equal.

• Adjacent angles sum to 180°.

Step-by-Step Calculation

1. Find ∠ADC: Since diagonal BD bisects ∠ADC, ∠ADC = 2 × ∠ADB = 2 × 25° = 50°.

2. Find ∠ABC: Opposite angles are equal, so ∠ABC = ∠ADC = 50°.

3. Find ∠BAD: Adjacent angles sum to 180°, so ∠BAD = 180° − ∠ABC = 180° − 50° = 130°.

4. Compute Expression: 2∠BAD − ∠ABC = 2(130°) − 50° = 260° − 50° = 210°.

Final Answer: 210°