Answer:
m∠C = 102°
Step-by-step explanation:
This is is a cyclic quadrilateral
• The sum of opposite angles in a cyclic quadrilateral is equal to 180°
m∠D + m∠B = 180°
m∠B = 180° - m∠D
m∠B = 180° - 80°
m∠B = 100°
If you look at the above diagram properly, you will notice there are are angles outside the circle. We refer to this an exterior or external angles in a cyclic quadrilateral
• Note that m∠B is Opposite the exterior angle m∠CDA
Hence,
m∠CDA = 2 × m∠B
m∠CDA = 2 × 100°
m∠CDA = 200°
• m∠CDA = m∠CD + m∠DA
m∠DA = m∠CDA - m∠CD
m∠DA = 200° - 116°
m∠DA = 84°
• Another external angle we need to find is m∠DAB
m∠DAB = m∠DA + m∠AB
We know that m∠DA = 84°, therefore,
m∠DAB = 84° + 120°
m∠DAB = 204°
• The final step is to solve for m∠C
m∠DAB is Opposite m∠C
Hence
m∠C = 1/2 × m∠DAB
m∠C = 1/2 × 204
m∠C = 102°
