An exterior angle of a triangle equals _______ minus the adjacent interior angle.

2 answers:

5 0

As isosceles triangle has two congruent sides with a third side
that is the base. 

A base angle of an isosceles triangle is one of the angles formed by 
the base and another side. Base angles are equal because of the 
definition of an isosceles triangle. 

A picture would probably help here: 

A 
. 
/ \ ABC = ACB = 39 degrees 
/ BAC = ??

._______________. 
B C 
base 
ABC is the isosceles triangle. AB is congruent to AC. Angle ABC 
is congruent to angle ACB. These are the base angles. 
Triangle is a convex polygon with three segments joining three non-collinear points. Each of the three segments is called a side, and each of the three non-collinear points is called a vertex. 
Triangles can be categorized by the number of congruent sides they have. For instance, a triangle with no congruent sides is a scalene triangle; a triangle with two congruent sides is an isosceles triangle; a triangle with three congruent sides is an equilateral triangle. 
Triangles can also be categorized by their angles. For instance, a triangle with three acute interior angles is an acute triangle; a triangle with one obtuse interior angle is an obtuse triangle; a triangle with one right interior angle is a right triangle; a triangle with three congruent interior angles is an equiangular triangle. 
One property of a triangle is that the sum of the measures of the three interior angles is always 180 degrees (or pi radians). In addition, the exterior angle of a triangle is the supplement of the adjacent interior angle. The measure of the exterior angle is also the sum of the measures of the two remote interior angles.

musickatia [10]3 years ago

3 0

Answer:

An exterior angle of a triangle equals 180° minus the adjacent interior angle.

Step-by-step explanation:

The two angles are said to be adjacent if they have a common vertex and a common side between them.

So, if an angle is exterior to any angle of a triangle, But that particular angle of a triangle is adjacent to the exterior angle. Then, The both angles must lie on the straight line and thus both will form a linear pair.

The measure of the linear pair is always supplementary.

⇒ Exterior angle + Adjacent interior angle = 180°

⇒ Exterior angle = 180° - Adjacent interior angle

Hence, An exterior angle of a triangle equals 180° minus the adjacent interior angle.

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