Question

Quadrilateral ABCD is Inscribed in circle O. what is m∠A​

Answer 1

m∠A = 121°

Explanation:

• Quadrilateral ABCD is Inscribed in circle with centre O.

• So, it is a cyclic quadrilateral.

• Opposite angles of a cyclic quadrilateral are supplementary.

• 
  `\implies` m∠B + m∠D = 180°

• 
  `\implies` (2x + 3)° + (4x + 3)° = 180°

• 
  `\implies` (6x + 6)° = 180°

• 
  `\implies` 6x + 6 = 180

• 
  `\implies` 6x = 180 - 6

• 
  `\implies` 6x = 174

• 
  `\implies` x = 174/6

• 
  `\implies` x = 29

• ∠A & ∠C are also opposite angles of the cyclic quadrilateral ABCD.

• 
  `\implies` m∠A + m∠C = 180°

• 
  `\implies` m∠A + (2x + 1)° = 180°

• 
  `\implies` m∠A + (2*29 + 1)° = 180°

• 
  `\implies` m∠A + 59° = 180°

• 
  `\implies` m∠A = 180° - 59°

• 
  `\implies` m∠A = 121°