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Marysya12
14 days ago
14

ABCD is a quadrilateral inscribed in a circle, as shown below: Circle O is shown with a quadrilateral ABCD inscribed inside it.

Angle A is labeled x plus 16. Angle B is labeled x degrees. Angle C is labeled 6x minus 4. Angle D is labeled 2x plus 16. What equation can be used to solve for angle C? (x + 16) + (x) = 180 (x + 16) + (6x − 4) = 180 (x + 16) − (2x + 16) = 180 (x + 16) + (x) = 90
Mathematics
1 answer:
PIT_PIT [3.9K]14 days ago
5 0

Answer:

B. (x + 16) + (6x − 4) = 180

Step-by-step explanation:

The Theorem of Cyclic Quadrilaterals states that in any quadrilateral located within a circle, the angles opposite to each other will sum to 180 degrees. Therefore, the conclusion can be drawn:

∠A + ∠C = 180° leading to (x + 16) + (6x - 4) = 180°

∠B + ∠D = 180° which equates to x + (2x - 16) = 180°

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