What is the value of w? a.40 b.52.5 c.75 d.100

The angles w and 80 are inscribed angles in the top left and bottom right corners respectively. They are opposite angles in this inscribed quadrilateral. Because they are opposite angles in the inscribed quadrilateral, they add to 180 degrees.

w+80 = 180
w+80-80 = 180-80
w = 100

Choice D

Remark
In a cyclic quadrilateral ( a four sided figure that can be drawn in a circle), the opposite sides add up to 180 degrees.

Consequence.
x + 105 = 180
w + 80 = 180

Solution
w + 80 = 180   Subtract 80 from both sides.
w = 180 - 80
w =  100 degrees Answer

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