2 Marks Questions

Question 12 Marks

Can a triangle have two obtuse angles? Give reason for your answer.

Answer

An angle whose measure is more than $90^\circ$ but less than $180^\circ$ is called an obtuse angle. A triangle cannot have two obtuse angles because the sum of all the angles of it cannot be more than $180^\circ.$ It is always equal to $180^\circ$

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Question 22 Marks

If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles? Give reason for your answer.

Answer

If two intersect each other at a point, then four angles are formed. If one of these four angles is a right angle, then each of the other three angles will also be a right by linear pair axiom.

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Question 32 Marks

How many triangles can be drawn having its angles as 53°, 64° and 63°? Give reason for your answer.

Answer

Infinitely many triangles,
The sum of given angles = 53° + 64° + 63° = 180°
Here, we see that sum of all interior angles of triangle is 180°, so infinitely many triangles can be drawn.

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Question 42 Marks

Can a triangle have all angles less than 60° ? Give reason for your answer.

Answer

A triangle cannot have all angles less than 60°. Then, sum of all the angles will be less than 180° whereas sum of all the angles of a triangle is always 180°.

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Question 52 Marks

Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle? Justify your answer.

Answer

No, each of these angles will be a right angle only they form a linear pair, i.e., when the non-common arms of the given two adjacent angles are two opposite rays & common arm is perpendicular to them.

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