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The sum of two exterior angles of an isosceles triangle is equal to 240°. What are the measures of the interior angles?

2 Answers

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Final answer:

The remaining exterior angle of the isosceles triangle is 120°, therefore the associated interior angle is 60°, and the triangle is equilateral with all interior angles being 60°.

Step-by-step explanation:

The sum of the exterior angles of a triangle is always equal to 360°. Given that the sum of two exterior angles is 240°, the remaining exterior angle must be 120° (since 360° - 240° = 120°). The interior angle is supplementary to the exterior angle in a triangle, meaning they add up to 180°. Therefore, the measure of the associated interior angle is 60° (since 180° - 120° = 60°). Because the triangle is isosceles, two of its interior angles are equal. The two equal interior angles are each 60°, and the third interior angle would be the one supplementary to the sum of the other two. This results in the third angle also being 60°, thus making the triangle equilateral as all interior angles are equal.

User Pforhan
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Let the two equal interior angles of the isosceles triangle be x and x.

Then, the corresponding exterior angles are 180 - x and 180 - x.

It is given that the sum of the exterior angles is 240°.

Therefore, (180 - x) + (180 - x) = 240

360 - 2x = 240

360 - 240 = 2x

2x = 120

x = 60°

Hence, the measures of each interior angles is 60°.

User Samuel Tan
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