Question

The angles of a cyclic quadrilateral
ABCD are ZA=(6x + 10), ZB = (5x),
ZC = (x + y) and ZD=(3y - 10). Find x
and y and then the values of the four angles.
​

Answer 1

$</p><p>\huge{\fbox{\fbox{\bigstar{\mathfrak{\blue{The \: four \: Angles \: Are \: 130°, \: 100°, \: 50°, \: and \: 80° respectively. }}}}}}$

In a cyclic Quadrilateral, the opposite angles are supplementary.

Hence

Angle A + Angle C = 180°

Angle B + Angle D = 180°

Hence,

7x + y + 10 = 180° ............ [ 1 ]

5x + 3y - 10 = 180° ............. [ 2 ]

Solving we get,

X = 20°

Y = 30°

Angle A = 130 °

Angle B = 100 °

Angle C = 50°

Angle D = 80°