Answer:
The m∠D is 98° ⇒ answer D
Step-by-step explanation:
* Lets revise some facts in the circle
- The quadrilateral is inscribed in a circle if its four vertices lie on the
circumference of the circle
- It is called a cyclic quadrilateral
- Every two opposite angles in it are supplementary means the
sum of their measures is 180°
∵ ABCD is inscribed in a circle
∴ ABCD is a cyclic quadrilateral
∵ ∠A and ∠C are opposite angles in the cyclic quadrilateral ABCD
∴ ∠A and ∠C are supplementary
∴ m∠A + m∠C = 180°
∵ m∠A = 64°
∵ m∠C = (9x - 1)°
∴ 64 + (9x - 1) = 180 ⇒ simplify
∴ 63 + 9x = 180 ⇒ subtract 63 from both sides
∴ 9x = 117 ⇒ divide both sides by 9
∴ x = 13
- Lets find the measure of ∠B
∵ m∠B = (6x + 4)°
∵ x = 13
∴ m∠B = 6(13) + 4 = 78 + 4 = 82°
- Lets find the measure of ∠D
∵ ∠B and ∠D are opposite angles in the cyclic quadrilateral ABCD
∴ ∠B and ∠D are supplementary
∴ m∠B + m∠D = 180°
∵ m∠B = 82°
∴ 82° + m∠D = 180° ⇒ subtract 82° from both sides
∴ m∠D = 98°
* The m∠D is 98°
