 Hello and welcome to the session. In this session, we discussed the following question which says two angles of an eight-sided polygon are 142 degrees and 176 degrees. If the remaining angles are equal to each other, find the magnitude of each of the equal angles. Before moving on to the solution, let's see what is the sum of the interior angles of a convex polygon of n sides. This is equal to 2n minus 4 right angles. This is the key idea that we use for this question. Let's proceed with the solution now. In the question we are given that in an eight-sided polygon we are given measures of two angles and the measures are 142 degrees and 176 degrees. We are also given the remaining angles are equal to each other. That is, the remaining six angles are equal to each other and we have to find the magnitude of each of the equal angles. First of all, we have sum of the interior angles of a polygon of eight sides is equal to 2 into 8. That is, in this in place of n, we put 8 minus 4 into 90 degrees. Since we know that one right angle is 90 degrees and this is further equal to 16 minus 4 into 90 degrees. That is 12 into 90 degrees or you can say we get this equal to 1080 degrees. That is, we have sum of the interior angles of a polygon of eight sides is equal to 1080 degrees. Now, sum of the given measures of two angles of the polygon is equal to 142 degrees plus 176 degrees. That is, this is equal to 318 degrees. Now, we know that in an eight sided polygon there would be eight angles and we have got the sum of the two angles of the eight sided polygon which is 318 degrees and in the question we have that the remaining six angles are equal to each other. So, we can now find sum of the remaining six angles of the polygon would be equal to sum of the interior angles of the polygon which is 1080 degrees minus sum of the two angles of the polygon which is 318 degrees and this comes out to be equal to 762 degrees. Now, since we have the remaining six angles are equal therefore the measure of each equal angle would be equal to 762 degrees divided by 6 and this comes out to be equal to 127 degrees. That is, the measure of each equal angle is equal to 127 degrees. Thus, magnitude of each of the equal angles is equal to 127 degrees. So, this is our final answer. This completes the session. Hope you have understood the solution of this question.