Mathematics
The diagonals AC and BD of a rectangle ABCD intersect each other at P. If ∠ABD = 50°, find ∠DPC.
Answer
The diagonals of a rectangle are equal and bisect each other.
∴ AP = BP
From figure,
In △ABP,
AP = BP
⇒ ∠PAB = ∠ABP = 50° (Angles opposite to equal sides are equal in isosceles triangle)
⇒ ∠PAB + ∠ABP + ∠APB = 180°
⇒ 50° + 50° + ∠APB = 180°
⇒ ∠APB = 180° - 100° = 80°.
⇒ ∠DPC = ∠APB = 80° (Vertically opposite angles are equal).
Hence, ∠DPC = 80°.
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