Q. 14.5( 25 Votes )

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

Answer :

Let us consider trapezium **PQRS** with **PQ||RS**.

According to the problem, it is given that **∠****P = 70 ^{0}**and

**∠**

**Q = 80**.

^{0}We know that the sum of adjacent angles between two parallel lines is **180 ^{0}**.

i.e, **∠****P +** **∠****S = 180 ^{0}** ...... - - (1)

**∠****Q +** **∠****R = 180 ^{0}**. ...... - (2)

Substituting the value of ∠P in eq(1) we get,

⇒ 70^{0} + ∠S = 180^{0}

⇒ ∠S = 180^{0} - 70^{0}

⇒ **∠****S = 110 ^{0}**.

Substituting the value of ∠Q in eq(2) we get,

⇒ 80^{0} + ∠R = 180^{0}

⇒ ∠R = 180^{0} - 80^{0}

⇒ **∠****R = 100 ^{0}**.

The values of **∠****S** and **∠****R** is**110 ^{0}** and

**100**.

^{0}Rate this question :

In the figure, PQRS is an isosceles trapezium; ∠SRP = 30°, and ∠PQS = 40°. Calculate the angles ∠RPQ and ∠RSQ.

Karnataka Board - Mathematics Part II

In a trapezium ABCD with AB ║ CD, it is given that AD is not parallel to BC. Is ΔABC ≅ ΔADC? Give reasons.

Karnataka Board - Mathematics Part IIIn a trapezium PQRS, PQ ║ RS; and ∠P = 70° and ∠Q = 80°. Calculate the measure of ∠S and ∠R.

Karnataka Board - Mathematics Part II