Question

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

Answer 1

1st angle is 50° 2nd is 50° and 3rd angle is 80°.

Answer 2

Given,

An exterior angle of a triangle is 100 degrees and its interior opposite angles are equal to each other.

To Find,

The measure of each angle of the triangle.

Solution,

We can solve the question as follows:

It is given that an exterior angle of a triangle is 100 degrees and its interior opposite angles are equal to each other. We have to find all the angles of the triangle.

$Exterior\: angle\: of\: a\: triangle = 100^{o}$

Since the interior angles are equal to each other, let them be x.

Now,

We know that the exterior angle of a triangle is equal to the sum of the opposite interior angles of the triangle.

$Exterior\: angle = Sum\: of\: interior\: opposite\: angles$

Therefore,

$100^{o} = x + x$

$100^{o} = 2x$

$x = \frac{100}{2} = 50^{o}$

Each interior angle is equal to 50 degrees.

Now,

The sum of all the interior angles of a triangle is equal to 180 degrees.

Two interior angles are equal to 50 degrees, let the third angle be equal to C. Therefore,

$50 + 50 + C = 180$

$100 + C = 180$

$C = 180 - 100 = 80^{o}$

Hence, the angles of the triangle are equal to 50, 50, and 80 degrees.