In the diagram, EFGH is a rectangle having diagonals intersecting at M with KM=ML. G₂ = 55° and M₃ = 60°. Calculate the size of: 7.1.1 M₂ 7.1.2 GML

In a rectangle EFGH, the diagonals bisect each other and are equal in length.
Therefore, $EM = MF = GM = HM$.

Since $FM = GM$ (half-diagonals of a rectangle), $\triangle FMG$ is an isosceles triangle.
We are given $\angle MGF = G_2 = 55^\circ$.
Therefore, the base angles of $\triangle FMG$ are equal: $\angle MFG = \angle MGF = 55^\circ$. (Reason: Base angles of an isosceles triangle are equal).

The sum of angles in a triangle is $180^\circ$.

From the diagram, $M_2$ represents $\angle EMH$. Angles $\angle EMH$ and $\angle FMG$ are vertically opposite angles.
Vertically opposite angles are equal.

Question 7.1.2 Calculate the size of $GML$.

Angles $\angle FMG$ and $\angle GMH$ are adjacent angles on a straight line (or angles on a straight line).
The sum of angles on a straight line is $180^\circ$.

From the diagram, $M_3$ represents $\angle HML$, and we are given $M_3 = 60^\circ$.

From the diagram, $\angle GMH$ is composed of $\angle GML$ and $\angle HML$.