Question

If PQRS is a trapezium such that PQ || RS, (angle)P: S = 3:2, (angle)Q : R = 7:2,
then find the angles of the trapezium.
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Answer 1

Answer:

P=108°, Q=140°,R=72°, S=40°

Step-by-step explanation:

Let the angles P and S be 3x and 2x

And angles Q and R be 7y and 2y.

Sum of all angles of a quadrilateral = 360°

3x+2x + 7y+2y = 360°

5x + 9y = 360°

Also,

PQ||RS,

Q+R = 180°= P+S ( Pair of co-interior angles)

7y+2y = 180° = 3x+2x

5x = 180°, 9y = 180°

x= 36° , y = 20°

Therefore,

angles are:

P=108°, Q=140°,R=72°, S=40°

Answer 2

Answer:

Angle P=108°

Angle Q=140°

Angle R=40°

Angle S=72°