Question

A quadrilateral ABCD has the given angle measures. Select all measurements which
could come from a cyclic quadrilateral.

A:
angle A is 90°, angle B is 90°, angle C is 90°, and angle D is 90°

B:
angle A is 80°, angle B is 80°, angle C is 100°, and angle C is 100°

C:
angle A is 70°, angle B is 110°, angle C is 70°, and angle D is 110°

D:
angle A is 60°, angle B is 50°, angleC is 120°, and angle D is 130°

E:
angle A is 50°, angle B is 40°, angle C is 120°, and angle D is 150°

Answer 1

Answer:

A:  angle A is 90°, angle B is 90°, angle C is 90°, and angle D is 90°

B:  angle A is 80°, angle B is 80°, angle C is 100°, and angle C is 100°

D:  angle A is 60°, angle B is 50°, angle C is 120°, and angle D is 130°

Step-by-step explanation:

The sum of opposite angles of a cyclic quadrilateral is 180°

It must satisfy the following:

A+C=180° and B+D=180°

Only choice A and B and D satisfy.

Answer 2

The correct options are options A, B, and D.

What is a cyclic quadrilateral?

A quadrilateral having all its corners on a circle plus opposite angles' sum is 180° called a cyclic quadrilateral.

A) ∠A =90°

∠B=90°

∠C =90°

∠D =90°

∠A + ∠C = 180°

∠B + ∠D =180°

So, this quadrilateral can come from a cyclic quadrilateral.

B) ∠A =80°

∠B=80°

∠C =100°

∠D =10 0°

∠A + ∠C = 180°

∠B + ∠D =180°

So, this quadrilateral can come from a cyclic quadrilateral.

Similarly, options C, D, and E also can be checked whether they can come from a cyclic quadrilateral or not.

C) Cannot come from a cyclic quadrilateral since ∠A + ∠C =140°≠180°.

D) ∠A + ∠C = 180°

∠B + ∠D =180°

So,  this quadrilateral can come from a cyclic quadrilateral.

E)Cannot come from a cyclic quadrilateral since∠A + ∠C = 170°≠180°.

Therefore, The correct options are options A, B, and D.

To get more about the cyclic quadrilateral visit:

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