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Question
ABCD is a rectangle. DB is extended to point P. ∠PBA = 140°. ∴ find ∠DBC.
Options
40°
50°
60°
45°
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Solution
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°
