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
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