Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, ∠O = 120°, ∠R = 105° and ∠A = 135°? If not, why?

Solution:

Given, ROAM is a quadrilateral.

RO = 4 cm, OA = 5 cm, ∠O = 120°, ∠R = 105° and ∠A = 135°

We have to determine if it is possible to construct a quadrilateral ROAM.

We know that the sum of all the angles of a quadrilateral is 360°.

Now, ∠O + ∠R + ∠A = 120° + 105° + 135°

= 225° + 135°

= 360°

This implies that the sum of three angles of a quadrilateral is 360°

Therefore, the quadrilateral cannot be constructed.

✦ Try This: Is it possible to construct a quadrilateral POND in which PO = 5 cm, ON = 7 cm, ∠O = 130°, ∠P = 100° and ∠N = 140°? If not, why?

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 197

Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, ∠O = 120°, ∠R = 105° and ∠A = 135°? If not, why?

Summary:

It is not possible to construct a quadrilateral ROAM in which RO=4 cm, OA = 5 cm, ∠O = 120°, ∠R = 105° and ∠A = 135°.

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