Question

The measure of one of the exterior angle of a triangle is twice of one of its interior opposite angle and name the type of the triangle justify your answer
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Answer 1

the type of triangle is Iscoceles
this is because of exterior angle theorem

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Answer 2

Theorem:   An exterior angle of a triangle is equal to the sum of the opposite interior angles.

In the figure above, drag the orange dots on any vertex to reshape the triangle. The exterior angle at B is always equal to the opposite interior angles at A and C.

Although only one exterior angle is illustrated above, this theorem is true for any of the three exterior angles.

A related theorem

Because an exterior angle is equal to the sum of the opposite interior angles, it follows that it must be larger than either one of them. Stated more formally:

Theorem: An exterior angle of a triangle is always larger then either opposite interior angle.

Drag the vertices of the triangle around to convince yourself this is so.