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In ΔABC if ∠A=70° and ∠B=70°, find the measure of exterior angle A.
110°
70°
30°
140°
110°
The exterior angle at vertex A is simply the supplementary angle to interior angle A, which is 180°−70°=110°.
In triangle ABC, angle A = 70 degrees and angle B = 70 degrees.
Exterior Angle=180°−Interior Angle
The exterior angle at vertex A is simply the supplementary angle to interior angle A, which is 180°−70°=110°.
Students often mistake the exterior angle formula as the sum of opposite interior angles (which applies to the exterior angle of the vertex being considered, but the exterior angle at vertex A is just 180−A).
Identify Interior Angle A
The problem states that in triangle ABC, the measure of angle A is 70 degrees.
∠A=70°
Apply Supplementary Angle Property
An exterior angle and its corresponding interior angle at the same vertex form a linear pair, which means they sum up to 180 degrees.
Exterior ∠A=180°−∠A
Calculate Value
Substitute the value of angle A into the equation to find the measure of the exterior angle.
Exterior ∠A=180°−70°=110°
A is correct because the exterior angle at vertex A is the supplement of interior angle A, calculated as 180° - 70° = 110°.
This concept is fundamental in Geometry for solving cyclic quadrilateral problems and parallel line transversal proofs.
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