Determine, with reasons, the following angles in terms of x: D1, D2, D3, D4, D5.

here are the solutions for Activity 3:

3.1 Determine, with reasons, the following angles in terms of $x$:

From the diagram, we observe two intersecting straight lines. Let's assume the line containing $\hat{D}_1$, $\hat{D}_2$, $\hat{D}_3$ is a straight line, and the line containing $\hat{D}_2$, $\hat{D}_5$ is another straight line.
This implies that $\hat{D}_1$ and $\hat{D}_4$ are vertically opposite angles, and $\hat{D}_2$ and $\hat{D}_5$ are vertically opposite angles.
Also, the angle marked $x$ at the top left is an