G7.1 The acute angle between the 2 hands of a clock at 3:30 a.m. is $p^{\circ}$. Find $p$.
G7.2 In $\triangle A B C, \angle B=\angle C=p^{\circ}$. If $q=\sin A$, find $q$.
G7.3 The 3 points $(1,3),(a, 5),(4,9)$ are collinear. Find $a$.
G7.4 The average of $7,9, x, y, 17$ is 10 . If $m$ is the average of $x+3, x+5, y+2,8, y+18$, find $m$.
Reference: 1985 FI3.1 1987 FG7.1, 1989 FI1.1, 1990 FG6.3, 2007 HI1
At 3:00 a.m., the angle between the arms of the clock $=90^{\circ}$
From 3:00 a.m. to 3:30 a.m., the hour-hand had moved $360^{\circ} \times \frac{1}{12} \times \frac{1}{2}=15^{\circ}$.
The minute hand had moved $180^{\circ}$.
$$
\begin{array}{l}
p=180-90-15=75 \\
\angle B=\angle C=75^{\circ}, \angle A=180^{\circ}-75^{\circ}-75^{\circ}=30^{\circ} \\
q=\sin 30^{\circ}=\frac{1}{2}
\end{array}
$$

Reference: 1984 FSG.4, 1986FG6.2, 1987 FG7.4, 1989 HG8
$$
\begin{array}{l}
\frac{9-5}{4-a}=\frac{9-3}{4-1}=2 \\
\Rightarrow a=2 \\
\frac{7+9+x+y+17}{5}=10 \\
\Rightarrow x+y=17 \\
m=\frac{x+3+x+5+y+2+8+y+18}{5} \\
=\frac{2(x+y)+36}{5}=14
\end{array}
$$