Question

In a trapezium PQRS, PQ ║ RS; and ∠P = 70° and ∠Q = 80°. Calculate the measure of ∠S and ∠R.

Answer 1

Answer:

∠R=100° and ∠S=110°

Step-by-step explanation:

Given: PQRS is a trapezium, PQ║RS, ∠P=70° and ∠Q=80°

From the figure, If PQ║RS, then ∠P+∠S=180° (Pair of adjacent angles of a trapezium are supplementary)

⇒70°+∠S=180°

⇒∠S=180°-70°

⇒∠S=110°

Also, ∠Q and ∠R forms the adjacent angle pair, therefore their sum equals 180°, hence, ∠Q+∠R=180°

⇒80°+∠R=180°

⇒∠R=180°-80°

⇒∠R=100°

Hence, ∠R=100° and ∠S=110°

Answer 2

Solution :

In trapezium PQRS ,

PQ//RS ,

<P = 70° , <Q = 80°

i ) <P + <S = 180°
________________
PQ // SR, SP is a transversal ,

Sum of interior angles

same side of the transversal are supplementary .
________________

70° + <S = 180°

=> <S = 180° - 70° = 110°

ii ) <Q + <R = 180°

=> 80° + <R = 180°

=> <R = 180° - 80° = 100°

Therefore

<S = 110° , <R = 100°

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