Question 202
Construct a trapezium RISK in which $R I ∥ K S$ , RI = 7 cm, IS = 5 cm, RK = 6.5 cm and $∠ I = 60^{\circ}$ .

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Solution

$∠ I + ∠ S = 180^{\circ}$
$60^{\circ} + ∠ S = 180^{\circ}$ [cointerior angles]
$∠ S = 120^{\circ}$
Steps of Construction
Step I Draw an arc RI = 7 cm.
Step II Make $∠ R I X = 60^{\circ}$ .
Step III With I as centre and radius 5 cm, draw an arc, cutting IX at S.
Step IV Make $∠ I S Y = 120^{\circ}$ .
Step V With R as centre and radius 6.5 cm, draw an arc cutting SY at K.
Step VI Join KR.
Thus, RISK is the required trapezium.

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