Question

If one of the angles of a triangle is 62, then the angle between the exterior bisectors of the other two angles is
(a) 31° (b) 59° (c) 121° (d) 118°

Answer 1

The angle between the exterior bisectors of the other two angles is 59°.

Step-by-step explanation:

We are given that one of the angles of a triangle is 62 and we have to find the angle between the exterior bisectors of the other two angles.

Firstly, as we know that the angle sum property of the triangle says: The sum of all three angles of the triangle is equal to 180°.

First angle + Second angle + Third angle = 180°

62° + Second angle + Third angle = 180°

So, Sum of other two angles = 180° - 62° = 118°

Now, it is given that the bisectors of both the other angles have been made and due to which the other two angles will get halved. So, if both the angles get halved then their sum will also get halved, that is;

Half of the sum of other two angles = $\frac{118}{2}$ = 59°

Hence, the angle between the exterior bisectors of the other two angles is 59°.