Can a triangle have
(i) Two right angles?     (ii) All angles less than 60o?

(iii) All angles equal to 60o?  (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 180o, where as the sum of three angles of a triangle is 180o.

(ii)  No. If each angle is less than 60o, then the sum of three angles will be less than 180o where as the sum of the three angles should be 180o.
(iii) Yes. If each angle is 60o, then the sum of the angles will be 180o. The triangle in this case will be equilateral.
(iv)Yes. The sum of two acute angles will be less than 180o. So the third angle is possible making the sum 180o.

Answered by  | 4th Jun, 2014, 03:23: PM