 Let's talk about exterior angle theorem for any given triangle. So let us understand what it is. Exterior angle theorem says that an exterior angle of any triangle is equal to the sum of other two interior angles. So I am just going to label this angle as x and then this angle as m and this angle as n. So according to exterior angle theorem for the triangle x is equal to m plus n. But how do we prove this? To prove this let's do some constructions. So first of all I will name the given triangle as triangle ABC first. Let's name this point as D so that we have the exterior angle as angle ACD and let's name this line as PQ. Now what we want to prove here is the interior angles CAB and CBA when summed up equal the exterior angle ACD. So what we need to prove is angle ACD is equal to angle CAB plus angle BAC. So now what we have done here is we have constructed a parallel line. So AB is parallel with PQ and we have constructed this line PQ through C. So AC acts as a transfer cell that cuts parallel lines AB and PQ. Now we have certain pair of angles that form when a transfer cell intersects two parallel lines. The angles that we see here so just to identify these angles I will name these angles as P and S and these angles would be named as 1 and 2. So angle 1 and angle T are equal. Why? Because these are alternate pair of angles. Similarly angle 2 is equal to angle S and that the reason behind it is that these are corresponding angles considering AB and PQ as parallel lines and BC as the transfer cell with BC intersecting AB and PQ it's a corresponding pair of angles. And now because these two are equal let's say this is equation 1 and this is equation 2 we can add equation 1 and 2. So angle 1 plus angle 2 is equal to angle T plus angle S right angle T and angle S is nothing but angle ACD and angle 1 plus angle 2 is nothing but angle 1 can be written as angle CAB plus angle 2 can be written as angle CBA and so we just proved that major of exterior angle of a triangle is equal to the two other interior angles of the triangle. Formally this statement can be written as an exterior angle of a triangle is equal to the sub-office interior opposite angles. The keyword opposite is important because if we are considering this as the exterior angle we cannot take this interior angle itself we have to take angle 1 and angle 2. Let's look at the problem based on this theorem. So the problem here is that if angle SPR is an exterior angle of triangle PQR find angle PQR. Now in this case from the exterior angle theorem we know that the exterior angle SPR should be equal to the internal opposite angles in the triangle. The opposite internal angles are angle PRQ and angle PQR. So angle PQR plus angle PRQ should equal angle SPR. We know the major of angle SPR which is given as 142 degrees and the major of angle PQR we don't know that we need to find out and we have been given with the major of angle PRQ which is 68 degrees. Now just rearranging to find angle PQR we subtract 68 from both sides and we just shifted angle PQR to the left we get angle PQR is equal to 142 degrees minus 68 degrees and that gives us angle PQR is equal to 74 degrees. And this is how we can apply exterior angle theorem to solve problems related to the exterior angles and angles inside the triangle.