Question

Can a triangle have:

(i) Two right angles?

(ii) Two obtuse angles?

(iii) Two acute angles?

(iv) All angles more than ${60}^{\circ }$?

(v) All angles less than ${60}^{\circ }?$

(vi) All angles equal to ${60}^{\circ }?$

Justify your answer in each case.

Answer 1

(i) In a triangle, two right-angles cannot be possible.We know that sum of there angels is ${180}^{\circ }$ and if there are two right-angles, then the third angle angel will be zero which is not possible.

(ii) In a triangle, two obtuse angle cannot be possible. We know that sum of the three angles of a triangle is ${180}^{\circ }$ and if there are two obtuse angle, then the third angle will be negative which is not possible.

(iii) In a triangle, two acture angles are possible as sum of three angles of a triangle is ${180}^{\circ }$.

(iv) All angles more than ${60}^{\circ }$,they are also not possible as the sum will be more than ${180}^{\circ }$

(v) All angles less than ${60}^{\circ }$.They are also not possible as the sum will be less than ${180}^{\circ }$

(vi) All angles equal to ${60}^{\circ }$ . This is possible as the sum will be ${60}^{\circ }\times 3={180}^{\circ }$.