Answer:
a = 20
b = 30
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