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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let the unknown angles be x
x+x=100(exterior angle property)
2x=100
x=100/2
x=50
Therefore, measure of both angles are equal I. e. 50
x+x=100(exterior angle property)
2x=100
x=100/2
x=50
Therefore, measure of both angles are equal I. e. 50
Answered by
2
Answer:
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
.
Step-by-step explanation:
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