Determine, with reasons, the size of angle M in triangle MNK given PQ || MK, angle KNM = 90 degrees, and angle MKN = 63 degrees. Also, find angles Q1 and Q2.

Here are the solutions for Activity 2:

2.1 Determine, with reasons, the size of:

Given information:

• $MN \perp KN \implies \angle KNM = 90^\circ$.
• $PQ \parallel MK$.
• $\hat{K} = 63^\circ \implies \angle MKN = 63^\circ$.
• From the diagram, $\angle Q_1 = \angle Q_2$ (indicated by single arcs).

First, let's find $\hat{M}$ using the sum of angles in $\triangle MNK$:
In $\triangle MNK$:

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