State true or false: A quadrilateral ROAM with RO = 4 cm, OA = 5 cm, ∠O = 120°, ∠R = 105° and ∠A = 135° can be constructed.

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True

False

answer is B.

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Detailed Solution

Here, the statement says that the quadrilateral with the mentioned dimensions and angle measures can be constructed and we have to state if it is true or not.
Now, we can observe that three angle measures for the quadrilateral are given and according to the angle sum property of a quadrilateral, the sum of all the interior angles of a quadrilateral is always

360 ∘

.
Now, taking the sum of all the angles of the quadrilateral ROAM and applying the angle sum property, we have,

∠ R + ∠ O + ∠ A + ∠ M = 360 ∘

Substituting the given values of the angle measures, we get,

105 ∘ + 120 ° + 135 ° + ∠ M = 360 ∘ 360 ∘ + ∠ M = 360 ° ∠ M = 360 ∘ − 360 ∘ ∠ M = 0 ∘

It can be observed that the measure of

∠ M

0 ∘

, which is not possible because then the sides AM and RM will coincide and the resulting shape won’t be a quadrilateral.
Therefore, the quadrilateral with the given dimensions can never be constructed.
Hence, the given statement is false.
Hence, the correct option is (2).

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