Find the value of each variable.

a = 20

b = 30

Step-by-step explanation:

1) Solving for a

From the diagram above, KL + ML = An arc

Hence, we add them up

110° + 130° = 240°

1/2 of 240° = 120°

Solving for a°

180° = 120° + 3a (sum of opposite angles in a cyclic quadrilateral)

180° - 120° = 3a

60° = 3a

a = 60/3

a = 20

2) Solving for b

The sum of the exterior angles of a circle = 360°

Hence:

360° = KL + ML + JM + JK

KL = 110°

ML = 130°

JM = 54°

JK = ??

JK = 360 - (110° + 130° + 54°)

JK = 360 - 294

JK = 66°

Adding up JK + JL = 54° + 66°

= 120°

1/2 of 120° = 60°

Hence:

60° + 4b = 180°(sum of opposite angles in a cyclic quadrilateral)

4b = 180° - 60°

4b = 120°

b = 120/4

b = 30

26

step-by-step explanation: