Respuesta :

The measure of angle BCD is 41° ⇒ answer a

Step-by-step explanation:

Let us explain what is the cyclic quadrilateral

  • It is a quadrilateral inscribed in a circle
  • Its vertices lie on the circumference of the circle
  • Its vertices are inscribed angles in the circle
  • Each two opposite angle of it are supplementary

Look to the attached figure

∵ ABCD is a cyclic quadrilateral

∴ ∠A and ∠C are supplementary

∴ ∠B and ∠D are supplementary

∵ The sum of the measures of the supplementary angle is 180°

∴ m∠A + m∠C = 180°

∴ m∠B + m∠D = 180°

∵ m∠BAC = 67°

∵ m∠CAD = 72°

∵ ∠A = ∠BAC + ∠CAD

∴ m∠A = 67 + 72 = 139°

∵ m∠DAB + m∠BCD = 180° ⇒ opposite ∠s in cyclic quadrilateral

∵ m∠DAB = 139°

∴ 139 + m∠BCD = 180

- Subtract 139 from both sides

∴ m∠BCD = 41°

The measure of angle BCD is 41°

Learn more:

You can learn more about circles in brainly.com/question/2115496

#LearnwithBrainly

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