Question

The diagonals AC and BD of a rectangle ABCD intersect each other at P. If ∠ABD = 50°, then ∠DPC = 

A. 70° 

B. 90° 

C. 80° 

D. 100°

Answer 1

Option : (C)

Given, 

ABCD is a rectangle

Diagonals AC & BD intersect each other at P 

∠ABD = 50° 

∵ diagonals of rectangle bisect each other and are equal in length 

=∠ABD = ∠PDC 

[alternate angles] 

∠PDC=∠PCD = 50° 

In ∆DPC, 

= ∠DPC + ∠PCD +∠PDC = 180° 

= ∠DPC + 50° + 50°= 180° 

= ∠DPC = 180°- 100° = 80°