PQRS is a cyclic quadrilateral. If ∠QPS = 75°,... | WAEC SSCE - General Mathematics - 2003 (Objective)

Question 1 Report

PQRS is a cyclic quadrilateral. If ∠QPS = 75°, what is the size of ∠QRS?

180^o

150^o

105^o

75^o

Answer Details

A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. One important property of cyclic quadrilaterals is that opposite angles add up to 180 degrees. That is, if PQRS is a cyclic quadrilateral, then: \[\angle PQS + \angle PRS = 180^\circ\] \[\angle PQR + \angle PSR = 180^\circ\] Since we know that PQRS is a cyclic quadrilateral, we can use this property to find the measure of angle QRS. Let x be the measure of angle QRS. Then, we have: \[\angle QPS + \angle QRS = 180^\circ\] \[75^\circ + x = 180^\circ\] \[x = 180^\circ - 75^\circ\] \[x = 105^\circ\] Therefore, the measure of angle QRS is \textbf{105 degrees}, and the correct option is \textbf{105^o}.}

Read lesson note on Polynomials (JAMB)

Read lesson note on Coordinate Geometry (JAMB)

Polynomials

Coordinate Geometry

View Answer

PQRS is a cyclic quadrilateral. If ∠QPS = 75°, what is the size of ∠QRS?

Related Questions

Download The App On Google Playstore