The sum of angles C and D must be 100 degrees, so that angles A, B, C and D add up to 360 degrees for the quadrilateral.
Half of the sum of 100 degrees (which is 50 degrees) must be the sum of the two bisected acute angles C and D. Two of those bisected angles form triangle DYC. That angle must therefore be 180-50 = 130 degrees at point Y.
It will be clearer if you draw yourself a picture. The angles C and D can be arbitratily drawn, but their sum has to be 100 degrees.
In a quadrilateral ABCD, Angle A = 120 degrees, Angle B = 140 degrees.
The bisectors of the angles C and D meet at the point Y.
What is the size of the angle DYC?
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bottom...he he he
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