Question

ABCD is a rectangle. DB is extended to point P. ∠PBA = 140°. ∴ find ∠DBC.

विकल्प

• 40°

• 50°

• 60°

• 45°

Answer 1

50°

Explanation:

Step 1: Find the measure of angle ABD

Since DB is extended to point P, P, B and D form a straight line. The angles on a straight line are supplementary, meaning they add up to 180°. Given that ∠PBA = 140°, we can find the measure of ∠ABD.

∠PBA + ∠ABD = 180°

140° + ∠ABD = 180°

∠ABD = 180° – 140°

∠ABD = 40°

Step 2: Use the properties of a rectangle

In a rectangle, all interior angles are right angles, so ∠ABC = 90°.

The angle ∠ABC is the sum of angles ∠ABD and ∠DBC.

∠ABC = ∠ABD + ∠DBC

Step 3: Solve for angle DBC

Substitute the known values of ∠ABC and ∠ABD into the equation from Step 2.

90° = 40° + ∠DBC

To find ∠DBC, subtract 40° from both sides:

∠DBC = 90° – 40°

∠DBC = 50°