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.​

Answer 1

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°.

Answer 2

$\huge { \sf{ \underline{ \underline \pink{Question}}}}$

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.

$\huge { \sf{ \underline{ \underline \pink{Answer}}}}$

Given:-

• Exterior angle = 100°
• Interior opposite angles are same

Calculation:-

Exterior angle = Sum of 2 interior angles

$100° = \frac{ \cancel{100}}{ \cancel2} = 50$

∴100° = 50 + 50