Question

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

Answer 1

Answer:

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

**************************************************

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