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  i) ∠AOB = 87°

  ii) ∠BOC = 72°

  iii) ∠COD = 123°

  iv) ∠AOD = 78°

Step-by-step explanation:

The first three angle measures can be read from the diagram. Find the rays that define the angle, and read the measure of the arc between them.

The last angle, AOD, is found using the fact that the sum of all of the angles around a point is 360°.

  87° +72° +123° +∠AOD = 360°

  ∠AOD = 360° -282° . . . . . . . . . . subtract 282° from both sides

  ∠AOD = 78°

3

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."