Two parallel roads JK JK\,JK and LM LM\,LM are connected by a path PNPNPN, where P P\,P is a junction on JK JK\,JK and N N\,N is on LMLMLM. The angle ∠LNP=110∘\angle LNP = 110^\circ∠LNP=110∘. A triangular park PQR PQR\,PQR is adjacent to the path such that the internal angles are ∠PRQ=30∘\angle PRQ = 30^\circ∠PRQ=30∘ and ∠PQR=50∘\angle PQR = 50^\circ∠PQR=50∘.
Find the size of angle xxx, which is the angle ∠QPK\angle QPK∠QPK.
Give a reason for each stage of your working.
Practise OCR GCSE Maths Angles in Parallel Lines with exam-style questions for Foundation and Higher tier. 32 questions, matched to the OCR GCSE Maths (J560) specification and written in the written papers style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.