Question

In quadrilateral ABCD. B = 80°. Bisectors of A and D meet at a point P.
If APD= 60°, find the measure of C.​
pls answer​

Answer 1

Answer:

Let the quadrilateral ABCD have the angles <A = 2a, <B = 2b, <C - 2c and <D = 2d.

The bisectors of <A and <B meet at M. So <AMB = 180 -a-b.

The sum of the four angles <A+<B+<C+<D + 360 deg = 2a+2b+2c+2d, or

a+b+c+d = 180 deg …(1)

we have seen that <AMB = 180-a-b = 180 -(a+b) …(2). Put the value of a+b from (1) in (2) to get

<AMB = 180 -[180-c-d] = 180 -180+c+d, or

<AMB = c+d = (1/2)[<C+<D]. Proved