NCERT Class 8 Mathematics Solutions: Chapter 3 –Understanding Quadrilaterals Exercise 3.3 Part 6

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Given this figure PQRS is inscribed in a circle

PQRS is Inscribed in a Circle

Question: 10 Explain how this figure is a trapezium. Which is its two sides are parallel?

Image:

Given Figure is Trapezium

Answer:

Here, [Sum of interior opposite angles is ]

Hence, KLMN is a trapezium.

Question: 11 Find in figure if AB || DC?

Image

A Figure is Quadrilateral and Find Value of Angle C

Answer:

Here,

Hence, the measure of .

Question: 12 Find the measure of ∠P and ∠S if SP || RQ in Figure. (If you find, is there more than one method to find?)

Image

In Given Quadrilateral Find∠Pand∠S

Answer:

Here,

Also,

Yes, one more method to find.

PQRS is a quadrilateral. Sum of measures of all angles is 360°.

So, we know the measurement of ∠Q, ∠R and ∠S.

[Angle sum property of quadrilateral]