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In a triangle ABC, if angle A = 40 degrees and angle B = 60 degrees, what is the measure of the exterior angle at vertex C?
100 degrees
80 degrees
120 degrees
140 degrees
100 degrees
Remember that the exterior angle at any vertex of a triangle is simply the sum of the two opposite interior angles; therefore, just add 40 and 60.
Angle A = 40 degrees, Angle B = 60 degrees. These are the two interior opposite angles to the exterior angle at vertex C.
Exterior Angle=∠A+∠B
Remember that the exterior angle at any vertex of a triangle is simply the sum of the two opposite interior angles; therefore, just add 40 and 60.
Students often spend time calculating the interior angle at C (180−40−60=80) and then subtracting that from 180 to find the exterior angle, which is a redundant extra step.
Identify the Exterior Angle Theorem
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 two interior opposite angles.
Ext \angle C=\angle A+∠B
Substitute the Given Values
Substitute the given values ∠A=40° and ∠B=60° into the theorem formula.
Ext \angle C=40°+60°
Calculate the Final Result
Add the values to find the exterior angle at vertex C.
Ext \angle C=100°
A is correct because the sum of the opposite interior angles 40 degrees and 60 degrees is 100 degrees.
This property is essential in Geometry for solving cyclic quadrilateral problems and finding angles in complex polygon configurations.
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