Question

One of the exterior angles of triangle is 100 degree. The interior opposite angles are equal to each other. Find the measure of these equal interior opposite angles.​

Answer 1

Answer:

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Step-by-step explanation:

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

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⇒∠A=50

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⇒∠B=50

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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

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.

Hence ∠A=50

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∠B=50

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∠C=80

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