Determine, with reasons, the size of angles based on the provided geometric diagram and information.

Here are the solutions for Activity 2:

2.1 Determine, with reasons, the size of:

Given information from the diagram and previous context:

• $MN \perp KN \implies \angle KNM = 90^\circ$.
• $PQ \parallel MK$.
• $\hat{K} = 63^\circ \implies \angle MKN = 63^\circ$.
• From the diagram, $\hat{Q}_1 = \hat{Q}_2$ (indicated by single arcs).
• The line $RQ$ is a straight line.
• $P$ is the intersection of $RQ$ and $MK$.
• $Q$ is a point on the line $PQ$.