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In ΔABC if ∠A=50° and ∠B=70°, find the measure of exterior angle A.
130°
140°
60°
30°
130°
The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Here, exterior angle at A = ∠B + ∠C. First, find ∠C = 180° - (50° + 70°) = 60°. Then, exterior angle A = 70° + 60° = 130°.
Triangle ABC has angles ∠A = 50° and ∠B = 70°.
∠Exterior A=∠B+∠C
The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Here, exterior angle at A = ∠B + ∠C. First, find ∠C = 180° - (50° + 70°) = 60°. Then, exterior angle A = 70° + 60° = 130°.
Many students mistakenly add the adjacent angle (∠A) to the exterior angle or calculate the supplement of ∠A without realizing ∠A's interior measure is 50°, meaning its supplement is 130° directly.
Calculate the third interior angle
In any triangle, the sum of internal angles is 180°. Given ∠A=50° and ∠B=70°, we find ∠C.
∠C=180°−(50°+70°)=60°
Apply Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the two opposite interior angles. For exterior angle at A, the remote angles are B and C.
Ext ∠A=∠B+∠C
Calculate final value
Substitute the known values into the equation to find the result.
Ext ∠A=70°+60°=130°
A is correct because the exterior angle at vertex A is equal to the sum of interior angles B and C, which is 70°+60°=130°.
This concept is fundamental to circle geometry theorems where exterior angles relate to arc properties and cyclic quadrilaterals.
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