In the diagram, ABTS and BDRT are circles. Name, giving a reason, another angle equal to: a) x b) y

Here are the solutions for the geometry problem:

9.2.1 Name, giving a reason, another angle equal to:

a) $x$
In the smaller circle ABTS, $\angle A$ (which is $x$) and $\angle B_2$ are angles subtended by the same arc ST.

$$\angle B_2 = x$$

Reason: Angles subtended by the same arc (ST) in circle ABTS.

$$\boxed{\angle B_2}$$

b) $y$
In the bigger circle BDRT, $\angle R_1$ (which is $y$) and $\angle T_1$ are angles subtended by the same arc