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

Question

The diagonals AC and BD of a rectangle ABCD intersect each other at P. If &#x2220; ABD =50&#xB0;, then &#x2220; DPC =

Philoid · Accepted Answer

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°