# Can a triangle have

(i) Two right angles? (ii) All angles less than 60^{o}?

(iii) All angles equal to 60^{o}? (iv)Two acute angles?

Justify your statement in each case.

### Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

(i) No. If a triangle has two right angles, the sum of two angles will be 180^{o}, where as the sum of three angles of a triangle is 180^{o}.

(ii) No. If each angle is less than 60

^{o}, then the sum of three angles will be less than 180^{o}where as the sum of the three angles should be 180^{o}.(iii) Yes. If each angle is 60

^{o}, then the sum of the angles will be 180^{o}. The triangle in this case will be equilateral.(iv)Yes. The sum of two acute angles will be less than 180

^{o}. So the third angle is possible making the sum 180^{o}.### Answered by | 4th Jun, 2014, 03:23: PM

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