Question

An exterior angle of a triangle is 100 and its interior opposite angles are equal to each other.
Find the measure of each angle of the triangle.
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Answer 1

Answer:

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

o

⇒∠B=50

o

Using angle sum property of a triangle,

Sum of all angles of a triangle =180

o

⇒∠A+∠B+∠C=180

o

⇒100+∠C=180

o

[from (1)]

⇒∠C=180

o

−100

o

⇒∠C=80

o

.

Hence ∠A=50

o

∠B=50

o

∠C=80

o

.

Answer 2

By theorem we know that

<A + <B = 100

interior opposite angles are equal to each other

<A = <B

<A + <A = 100

2 <A = 100

<A= 100 /2

<A= 50 degree

<B= 50

100 + <C = 180

<C = 180 - 100

<C = 80