Question

question 5 of 10

true or false? adjacent (or side-by-side) angles of a quadrilateral in a circumscribed circle are always supplementary.

a. true
b. false

Explanation:

Analyze the definition of a quadrilateral in a circumscribed circle

A quadrilateral in a circumscribed circle is an inscribed quadrilateral (also known as a cyclic quadrilateral), meaning all four of its vertices lie on the circle.

Evaluate the angle properties of cyclic quadrilaterals

According to the Inscribed Quadrilateral Theorem, the opposite angles of an inscribed quadrilateral are supplementary (their sum is \(180^\circ\)). Adjacent (side-by-side) angles are not necessarily supplementary unless the quadrilateral is a specific type, such as an isosceles trapezoid or a rectangle.

Determine the truth value of the statement

Since adjacent angles of a cyclic quadrilateral are not always supplementary, the statement is false.

Answer:

• A. True
• B. False (Correct answer)