in triangle pqr a and b are respectively the mid-points of sides pq & qr if angle pab = 60degree then angle pqr=?

Sure, let's solve the problem step by step.

Step 1: Draw triangle PQR on a piece of paper.

Step 2: Label the midpoints of sides PQ and QR as points A and B, respectively.

Step 3: Draw a line segment from point P to point A, and another line segment from point P to point B.

Step 4: Since A and B are midpoints, line segment PA is equal in length to line segment AQ, and line segment PB is equal in length to line segment BR.

Step 5: Since angle PAB is given as 60 degrees, draw a line segment from point A to point B.

Step 6: Now, we have a triangle PAB with angle PAB equal to 60 degrees.

Step 7: Since PA is equal in length to AQ, and PB is equal in length to BR, triangle PAB is an isosceles triangle.

Step 8: In an isosceles triangle, the angles opposite to the equal sides are also equal.

Step 9: Therefore, angle APB is also equal to 60 degrees.

Step 10: Now, let's look at triangle PQR. We know that angle PAB is equal to 60 degrees.

Step 11: Since angle PAB is an exterior angle of triangle PQR, it is equal to the sum of the two opposite interior angles.

Step 12: Let's denote angle PQR as x. Therefore, angle PQR + angle QRP = angle PAB.

Step 13: Substituting the values, we have x + x = 60 degrees.

Step 14: Simplifying the equation, we get 2x = 60 degrees.

Step 15: Dividing both sides by 2, we find that x = 30 degrees.

Step 16: Therefore, angle PQR is equal to 30 degrees.

So, angle PQR is 30 degrees.