Question

one of the exterior angles of a triangle is 100 degrees and its interior opposite angles is equal to each other. what is the measure of each of these two angles?

Answer 1

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Using the theorem that if the side of a triangle is produced then the interior angle is equal to the sum of two interior opposite angles of the triangle.

Let ΔABC be a triangle where the side BC is produced.

By the theorem we have

∠A+∠B=100

o

…………..(1)

It is given that the interior opposite angles are equal i.e., ∠A=∠B.

∴ Equation (1) becomes

2∠A=100

o

⇒∠A=50

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⇒∠B=50

o

Using angle sum property of a triangle,

Sum of all angles of a triangle =180

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⇒∠A+∠B+∠C=180

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⇒100+∠C=180

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[from (1)]

⇒∠C=180

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−100

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⇒∠C=80

o

.

Hence ∠A=50

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∠B=50

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∠C=80

o