Exterior Angle Theorem
when a triangle’s side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle.
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
In a triangle, an exterior angle is an angle formed by extending one of the sides of the triangle. Remote interior angles are the two angles that are inside the triangle and opposite the exterior angle.
For example, in the triangle ABC below:
“`
B
/ \
/ \
/ \
A———-C
“`
– Angle BAC is the exterior angle.
– Angle C and angle A are the remote interior angles.
According to the Exterior Angle Theorem, the measure of angle BAC is equal to the sum of the measures of angle A and angle C.
In mathematical notation, this can be expressed as:
“`
m< BAC = m< A + m< C
```
This theorem can be applied to any triangle, regardless of its shape or size.
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