Question

I'm kinda lost in this problem. Can you teach me how to solve these ​

Answer 1

53) Vertical angles are congruent, so $m\angle IDA=121^{\circ}$

54) $\angle YDA$ and $\angle YDF$ are supplementary, so $m\angle YDA=180^{\circ}-121^{\circ}=59^{\circ}$

55) Because vertical angles are congruent, $m\angle FDI=59^{\circ}$. Now, because DR bisects $\angle FDI$, this means $m\angle RDI=\frac{59}{2}=29.5^{\circ}$

56) This is a geometric sequence where the next term is obtained by multiplying the previous term by -2, so the next two numbers are 16, -32