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
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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
