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The diagonals A C\ a n d\ B D of a recta...

The diagonals `A C\ a n d\ B D` of a rectangle `A B C D` intersect each other at `Pdot` If `/_A B D=50^@,` then `/_D P C=` `70^@` (b) `90^@` (c) `80^@` (d) `100^@`

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Given : ABCD is a rectangle
As we know that the diagonals of rectangle are same and bisect each other. `AP=BP`
`anglePAB=anglePBA`(Equal sides have equal opposite angles)
`anglePAB=50^@`
Now, In `triangleAPB`
`angleAPB+angleABP+angleBAP=180^@`
`angleAPB+50^@+50^@=180^@`
`angleAPB=180^@`
...
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