Answer:
Explanation:
Yes, that is correct. The measure of the exterior angle of a triangle is equal to the sum of the two remote interior angles. In other words, if you extend one side of a triangle to form an exterior angle, then the measure of that exterior angle is equal to the sum of the measures of the two interior angles that are not adjacent to the exterior angle. This property is known as the Exterior Angle Theorem.
Mathematically, we can express this as:
Exterior angle = Sum of remote interior angles
Or, in symbols:
∠ABC = ∠A + ∠C
where ∠ABC is the exterior angle formed by extending side BC of triangle ABC, and ∠A and ∠C are the two remote interior angles.
Here are two more examples that illustrate the Exterior Angle Theorem:
Example 1:
Consider a triangle ABC with angles A, B, and C as shown below. If we extend side AC to form an exterior angle, then we can label the exterior angle as ∠DCE. The remote interior angles are ∠B and ∠A.
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C
/ \
/ \
/ \
/ \
/ \
/______\
A B
D
According to the Exterior Angle Theorem, we have:
∠DCE = ∠B + ∠A