Question

If the exterior angle of a triangle is 140 degrees and its interior opposite angles
are equal, what will be the measure of each interior opposite angle?

Answer 1

Answer:

• The required interior angles are 70°, 70° and 40°

Given:

• If the exterior angle of a triangle is 140 degrees and its interior opposite angles are equal,

To Find:

• Measure of each interior opposite angle?

Solution:

~Here we are given exterior angle of the Traingle 140°. We know that Exterior angle is the sum of interior angles. So let the interior opposite angle be x.

➞ x + x = 140°

➞ 2x = 140°

➞ x = 140/2

➞ x = 70°

• The required interior angles are 70° and 70°

Hence, we get the two interior angles and now we have to find the third angle. Sum of all angles of traingle is 180°

➞ 70 + 70 + x = 180°

➞ 140 + x = 180

➞ x = 180 - 140

➞ x = 40°

Hence,

• The required interior angles are 70°, 70° and 40°

Answer 2

✰ Given :

• Exterior angle of triangle = 140°
• It's interior angles are equal
• Find the measure of each interior opposite angle.

✰ Solution :

Let the interior opposite angle be x.

We know that,

Sum of interior angles is equal to exterior angle.

So,

➪ x + x = 140°

➪ 2x = 140°

➪ x = 140°/2

➪ x = 70°

Therefore, the interior opposite angles of the triangle = 70° and 70° (given that interior opposite angles are equal)

Let's check :

Angel A + Angle B + Angle C = 180°

(Angle sum property)

70° + 70° + Angle C = 180°

140° + Angle C = 180°

Angle C = 180° - 140°

Angle C = 40°

So,

70° + 70° + 40° = 180°

(Angle sum property)

180° = 180°

LHS = RHS

As the sum of all angels of the given triangle came out to be 180° after submitting the measure of the angles from our answer. We can say that the interior opposite angles of the triangle are 70° and 70°.

✰ Answer :

• Each interior opposite angles of the triangle are 70° and 70°.