Cyclic quadrilateral WISH, find all angle sizes.

Question

Let WISH be a cyclic quadrilateral, and K be the intersection of its diagonals WS

and HI. Given that arc WI is 100 degrees and arc SH is 80 degrees, and the sizes of as

many angles in the figure as you can.

Answer 1

All the angles of the quadrilateral can be determined.

You will easily be able to determine that the diagonals intersect at right angles.

∠SWH and ∠SIH are measured by the arc of 80º

Then ∠WHI and ∠WSI are measured by the arc of 100º

Those angles give you the information necessary to determine that the diagonals are perpendicular.

The acute angles in the other 2 right triangles will satisfy 4 simultaneous linear equations in 4 unknowns.

Remember that the opposite angles in a cyclic quadrilateral ae supplementary!

7/6/22 9:53 PM and

My answer is only partially correct.

The four angles measured by the given arcs, obviously can be determined; this shows that the diagonals are perpendicular.

The angles in the other 2 right triangles can be determined...but not in any simple fashion.