Now You Try!

You just learned that when a quadrilateral is inscribed inside a circle, the opposite angles are supplementary. That means that the measures of the opposite angles have a sum of 180°. Now, work through the following flashcards to practice solving problems with quadrilaterals that have been inscribed in a circle. Make sure to turn the flashcard over to check your work.

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Quadrilateral is inscribed in the circle

Quadrilateral ABCD is inscribed in the circle. Which pairs of angles are supplementary?

Since the quadrilateral is inscribed in the circle, the opposite angles are supplementary. That means angles A and C are supplementary, and angles B and D are supplementary.

Quadrilateral is inscribed in the circle

Quadrilateral ABCD is inscribed in a circle. Angle A measures 50°. What is the measure of angle C?

Angles A and C are opposite; therefore, they are supplementary. You can write and solve the following equation:

50° + m∠C = 180°

m∠C = 130°

Quadrilateral is inscribed in the circle

Quadrilateral ABCD is inscribed in a circle. The measure of angle D is 120°. What is the measure of angle B?

Angles B and D are opposite; therefore, they are supplementary. You can write and solve the following equation:

120° + m∠B = 180°

m∠B = 60°

Quadrilateral is inscribed in the circle

Quadrilateral ABCD is inscribed in a circle. Angle A measures (x + 15)° and angle C measures (3x - 10)°. Find x.

Since angles A and C are opposite, they are also supplementary. You can write and solve the following equation:

(x + 15) + (3x - 10) = 180

4x + 5 = 180

4x = 175

x = 43.75

Cards remaining:

Now, it's your turn to solve problems relating to quadrilaterals inscribed in a circle.