ANSWER
YES
Step-by-step explanation
We want to know if the exterior angle of a triangle can everbe equal to the measure of its adjacent interior angle.
Let me draw a diagram to explain.
y there is the exterior angle.
x is the adjacent interior angle.
We know that x and y must sum up to give 180 degrees (angle on a straight line).
In some triangles, namely Isoceles, scalene and equilateral triangle, the exterior angle is never equal in size to the adjacent interior angle.
The only kind of triangle that has this is a right-angled triangle.
Let me show you:
In this case, x = 90 degrees.
Following that angles on a straight line must add up to 180 degrees, we have that:
x + y = 180
=> 90 + y = 180
=> y = 180 - 90
y = 90 degrees
We see that x and y are equal.
So, YES. The measure of an exterior angle of a triangle can be equal to the measuere of its adjacent interior angle.