Question

c) find the number of right angles turned through by the hour hand of the clock when it goes from:
i) 1 to 10
ii) 9 to 3
iii) 5 to 8

1. create a set of flash cards on types of angles using ice cream sticks or straws and define the angles. (students can work in pairs to do this activity.)

Explanation:

Step1: Recall angle covered by hour - hand per hour

The hour - hand of a clock covers an angle of $30^{\circ}$ in 1 hour (since a full - circle is $360^{\circ}$ and there are 12 hours on a clock face, so $\frac{360^{\circ}}{12}=30^{\circ}$ per hour), and a right - angle is $90^{\circ}$.

Step2: Calculate number of hours passed for 1 to 10

The number of hours passed from 1 to 10 is $10 - 1=9$ hours. The angle covered by the hour - hand is $30^{\circ}\times9 = 270^{\circ}$. The number of right - angles is $\frac{270^{\circ}}{90^{\circ}} = 3$.

Step3: Calculate number of hours passed for 9 to 3

The number of hours passed from 9 to 3: We can calculate it as $(12 - 9)+3=6$ hours. The angle covered by the hour - hand is $30^{\circ}\times6 = 180^{\circ}$. The number of right - angles is $\frac{180^{\circ}}{90^{\circ}} = 2$.

Step4: Calculate number of hours passed for 5 to 8

The number of hours passed from 5 to 8 is $8 - 5 = 3$ hours. The angle covered by the hour - hand is $30^{\circ}\times3=90^{\circ}$. The number of right - angles is $\frac{90^{\circ}}{90^{\circ}} = 1$.

Answer:

i) 3
ii) 2
iii) 1