Question: Diagram NOT accurately drawn AB and CPD are parallel straight lines. PQ and PR are straight lines. (a) (i) Find the value of x. x = .. (ii) Give a reason for your answer. (b) (i) Find the value of y. (ii) Give a reason for your answer. top-left: a slanted line PQ crosses the upper parallel line AB at an angle of 62\u00b0, and a slanted line PR crosses AB at an angle of 71\u00b0; both lines meet at point P on the lower parallel line CPD. bottom-left: angle x\u00b0 is at point P between line CPD and PQ on the left side. bottom-right: angle y\u00b0 is at point P between line CPD and PR on the right side.

1. **Problem Statement:** We have two parallel lines AB and CPD. Lines PQ and PR intersect these parallel lines. Given angles at AB are 62\u00b0 (with PQ) and 71\u00b0 (with PR). We need to find angles $x$ and $y$ at point P on line CPD. 2. **Important Rule:** When a transversal crosses parallel lines, alternate interior angles are equal. Also, angles on a straight line sum to 180\u00b0. 3. **Find $x$:** - Angle between PQ and AB is 62\u00b0. - Since AB \parallel CPD and PQ is a transversal, angle $x$ at P (between PQ and CPD) is alternate interior angle to 62\u00b0. - Therefore, $x = 62$. 4. **Reason for $x$:** - $x$ equals 62 because alternate interior angles between parallel lines are equal. 5. **Find $y$:** - Angle between PR and AB is 71\u00b0. - Angles on a straight line sum to 180\u00b0. - At point P on AB, the angle adjacent to 71\u00b0 on the straight line is $180 - 71 = 109$. - Since AB \parallel CPD and PR is a transversal, angle $y$ at P (between PR and CPD) is alternate interior angle to 109\u00b0. - Therefore, $y = 109$. 6. **Reason for $y$:** - $y$ equals 109 because it is an alternate interior angle to the adjacent angle on AB, which is supplementary to 71\u00b0. **Final answers:** $$x = 62$$ $$y = 109$$