Question

ABCD is a cyclic quadrilateral (inscribed quadrilateral). Find the value of x and the measures of all the angles.

Answer 1

Explanation:

The "trick" to this problem is knowing that opposite sides of the box add up to 180°

Now that you know that maybe you can solve this?

180= 7x+2 + 6x-4

180 = 13x -2

182 = 13x

14 = x

find y now to find all the angles

180 = 2y + 4 +4y - 4

180 = 6y

30 = y

now solve the x expressions and the y expressions

7x+2

7(14)+2

98 + 2

D= 100°

6x-4

6(14)-4

84-4

B = 80°

2y + 4

2(30) + 4

60 + 4

A = 64°

4y-4

4(30)-4

120-4

C = 116°