Advertisements
Advertisements
Question
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?
Advertisements
Solution
Given measures are OA = 5 cm, ∠O = 120°, ∠R = 105° and ∠A = 135°
Here, we see that, ∠O + ∠R + ∠A = 120° + 105° + 135° = 360°
i.e. the sum of three angles of a quadrilateral is 360°.
This is impossible, as the total sum of angles is 360° in a quadrilateral.
Hence, this quadrilateral cannot be constructed.
APPEARS IN
RELATED QUESTIONS
Construct the following quadrilaterals.
Rectangle OKAY
OK = 7 cm
KA = 5 cm
Construct a quadrilateral ABCD in which AB = 3.8 cm, BC = 3.0 cm, AD = 2.3 cm, AC = 4.5 cm and BD = 3.8 cm.
Construct a quadrilateral ABCD, given that AB = 8 cm, BC = 8 cm, CD = 10 cm, AD = 10 cm and ∠A = 45°.
Construct a quadrilateral PQRS, in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, ∠Q = 75° and ∠R = 120°.
Construct a quadrilateral ABCD given BC = 6.6 cm, CD = 4.4 cm, AD = 5.6 cm and ∠D = 100° and ∠C= 95°.
Construct a quadrilateral ABCD when BC = 5.5 cm, CD = 4.1 cm, ∠A = 70°, ∠B = 110° and ∠D = 85°.
Construct a quadrilateral ABCD, where ∠A = 65°, ∠B = 105°, ∠C = 75° BC = 5.7 cm and CD = 6.8 cm.
Construct the following quadrilaterals with the given measurements and also find their area.
AGRI, AG = 4.5 cm, GR = 3.8 cm, ∠A = 60°, ∠G = 110° and ∠R = 90°
In a parallelogram PQRS, if ∠P = 60°, then other three angles are ______.
A quadrilateral can be constructed uniquely if three angles and any two sides are given.
