Answer: Angle C = 80
Step-by-step explanation:
Here, Quadrilateral ABCD is inscribed in circle.
Angle A = 2x+4
Angle B = 2x-1
Angle D = 3x-59
Quadrilateral ABCD is inscribed in circle.
Therefore,The Summation of opposite sides are supplementary and equal to 180.
Angle D + Angle B = 180
(3x-59) + (2x-1) = 180
5x - 60 = 180
5x = 240
x= 48
We know, Sum of all interior angle of Quadrilateral is 360
Angle A + Angle B + Angle C +Angle D = 360
(2x+4) + (2x-1) + Angle C + 3x-59= 360
7x - 56 + Angle C = 360
7x + Angle C = 416
Angle C = 416 - 7x
Angle C = 416 - 7×48
Angle C = 416 -336
