Question

The measure of an exterior angle of a triangle is equal to which of the following measures?

The measure of its complementary angle
The measure of its adjacent angle
The sum of the measures of the interior angles
The sum of the measures of its remote interior angles

Answer 1

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

Step-by-step explanation:

The correct answer is: The sum of the measures of its remote interior angles.

Here's why:

Exterior angle: An exterior angle of a triangle is formed when one side of the triangle is extended. It is the angle between the extended side and the adjacent side.

Remote interior angles: In a triangle, the two interior angles that are not adjacent to the exterior angle are called remote interior angles.

Theorem: The exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. This is known as the Exterior Angle Theorem.

Therefore, the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

Answer 2

The sum of the measures of its remote interior angles

Step-by-step explanation:

Let the triangle be ABC with their angles AB BC CA and

angle a, b and c.

We know that sum of angles of triangle is 180

so a + b + c = 180

=> a = 180 - (b + c) equation 1

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Now lets find the value for exterior angle of angle a.

we know that sum of angle on straight line 180 degree

as angle a and its exterior angle lie on straight line

therefore => angle a + exterior angle a = 180

=> exterior angle a = 180 - a

substituting value angle a from equation 1

exterior angle a = 180 - (180 - (b + c))

=> exterior angle a = b + c ( angle b and angle c are remote exterior angle to exterior angle a)

similarly we can perform above steps to find exterior angle b and exterior angle c which will be sum of measures of its respective remote interior angles

Thus we see that value of exterior angle is sum of measure of its remote interior angles