Question

Quadrilateral ABCD ​ is inscribed in circle O.

What is ​ m∠C ​ ?



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°

Answer 1

Opposite angles of a cyclic quadrilateral are supplementary

• m<B+m<D=180
• 2x+3+4x+3=180
• 6x+6=180
• 6x=174
• x=29

m<C

• 2x+1
• 58+1
• 59°

Answer 2

• 59°

Explanation:

• ∠C and ∠A are supplementary angles so as ∠B with ∠D, as opposite angles of a cyclic quadrilateral.
• Supplementary angles sum to 180°

First find the value of x:

• 2x + 3 + 4x + 3 = 180
• 6x + 6 = 180°
• 6x = 174°
• x = 29°

Find the measure of ∠C:

• m∠C = 2*29° + 1° = 59°