Question

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

Answer 1

Answer:

angles of the triangle are 50°, 50° and 80°

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Answer 2

Answer :

Measure of each angle of triangle is 80°, 50° and 50°.

Step-by-step explanation:

Given :-

Measure of exterior angle of triangle is 100°.

Opposite angles of triangle are equal.

To find :-

Measure of each angle of triangle.

Solution :-

Let, Angles of triangle be ∠1, ∠2 and ∠3.

It is given angle opposite to 100° are equal.

So, ∠1 = ∠2

Sum of all angles forms on straight line is equal to 180° [We can say by linear pair]

$\leadsto⇝ ∠3 + 100° = 180°$

$\leadsto⇝ ∠3 = 180° - 100°$

$\leadsto⇝ ∠3 = 80°$

Measure of ∠3 is 80°.

Now,

By Angle sum property of triangle:

$\leadsto⇝ ∠1 + ∠2 + ∠3 = 180°$

Put ∠1 = ∠2 and ∠3 = 80°.

$\leadsto⇝ ∠1 + ∠1 + 80° = 180°$

$\leadsto⇝ 2∠1 = 180° - 80°$

$\leadsto⇝ 2∠1 = 100°$

$\leadsto⇝ ∠1 = 100°/2$

$\leadsto⇝ ∠1 = 50°$

Measure of ∠1 is 50°.

∠1 = ∠2

So,

Measure of ∠2 is 50°.

Therefore,

Measure of each angle of triangle is 80°, 50° and 50°.