Quadrilaterals
Class 9 NCERT Exemplar Problems and Solutions
Question 1: If angles A,B,C and D of a quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4 then ABCD is a trapezium. Is this statement true? Give reason for your answer.Solution: Since, the angles are in the ratio 3:7:6:4,
Let these angles be 3x,7x,6x and 4x.
∵Since sum of angles of a quadrilateral is 360°,
∴3x+7x+6x+4x=360°
⇒ 20x=360°
⇒x=18°
∴The angles are:
∠A=3×18°=54°,
∠B=7×18°=126°,
∠C=6×18°=108° and
∠D=4×18°=72°
Since ∠A+∠B=54°+126°=180°. Thus, the sum of co-interior angles is 180°formed by lines AD,BC and transversal AB, ∴, AD∥BC.
So,ABCD is a trapezium.
Hence, the given statement is true.