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2 years ago

ABCD is a quadrilateral inscribed in a circle, as shown below:

Mathematics

1 answer:

Virty [35]2 years ago

3 0

The sum of the angles ∠B and ∠D will be 180°. Then the correct option is A.

<h3>What is a cyclic quadrilateral?</h3>

If the quadrilateral is inscribed in a circle then the quadrilateral is known as a cyclic quadrilateral.

Circle O is shown with a quadrilateral ABCD inscribed inside it.

Angle A is labeled x + 16.

Angle B is labeled x.

Angle C is labeled 6x - 4.

Angle D is labeled 2x + 16.

We know that the sum of the opposite angles of the cyclic quadrilateral is 180 degrees. Then we have

Then the sum of the angles ∠A and ∠C will be 180°.

∠A + ∠C = 180°

(x + 16)° + (6x - 4)° = 180°

Then the sum of the angles ∠B and ∠D will be 180°.

∠B + ∠D = 180°

(x)° + (2x + 16)° = 180°

Thus, the correct option is A.

More about the cyclic quadrilateral link is given below.

brainly.com/question/15061291

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