Question

Quadrilateral PQRS is inscribed in circle A. Which statement is necessarily true?

A.

m∠R = m∠S


B.

m∠R + m∠S = 180°


C.

m∠R = m∠S


D.

m∠R + m∠S = m∠P + m∠Q

Answer 1

A. m∠R = m∠S

Explanation:

Opposite angles of a cyclic quadrilateral add up to 180 degrees so m<R = 180-92 = 88 and m < S = 180-92 = 88 degrees.

Answer 2

(B) m∠R+m∠S=180°

Explanation:

The quadrilateral is inscribed in circle A, then m∠R+m∠S=180° as the sum of corresponding angles of a quadrilateral is equal to 180°.

Since, ∠R and ∠S are corresponding angles of the quadrilateral, therefore, they ca't be equal. Hence, ∠R≠∠S.

Also, the sum of all the angles of the quadrilateral is equal to 360°, therefore ∠P+∠Q+∠R+∠S=360°, hence ∠R+∠S≠∠P+∠Q

Therefore, option B is correct.