Are the exterior angles formed at each vertex equal? What can you say about the sum of an exterior angle of a triangle and its adjacent interior angle? What can you say about each of the interior opposite angles when the exterior angles is a right angle, an obtuse angle and an acute angle? Can the exterior angle of a triangle be a straight angle?

Dear Student,

Please find below the solution to the asked query:

1 ) All external angles in triangle only be equal if our triangle is an equilateral triangle . Otherwise we get different external angles .

2 ) Sum of exterior angles of triangle is 360$°$ .  and sum of external angle and its adjacent interior angle is 180$°$ .

3 ) We know from external angle theorem that  An measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles ( Opposite angles ) .

If external angle is right angle so . sum of the measures of the two non - adjacent interior angles ( Opposite angles ) = right angle ( 90$°$ ) .

If external angle is obtuse angle so . sum of the measures of the two non - adjacent interior angles ( Opposite angles ) = obtuse angle  ( More than 90$°$ ) .

If external angle is acute angle so . sum of the measures of the two non - adjacent interior angles ( Opposite angles ) = acute angle  ( Less than 90$°$ ) .

4 )  External angle of triangle never be straight line ( 180$°$ ) .

Hope this information will clear your doubts about topic.
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