Look at the right-angled triangle ABC. A
320
B
С
The square fits exactly inside the triangle.
Work out the sizes of angles x, y and z.

∠x = 90°

∠y = 58°

∠z = 32°

Step-by-step explanation:

The dimensions of the angles given are;

∠B = 32°

Whereby ΔABC is a right-angled triangle, and the square fits at angle A, we have;

∠A = 90°

∴ ∠B + ∠C = 90° which gives

32° + ∠C = 90°

∠C = 58°

∠x + Interior angle of the square = 180° (Sum of angles on a straight line)

∴ ∠x + 90° = 180°

Hence;

∠x = 90°

∠x + ∠y + 32° = 180° (Sum of angles in a triangle)

∴ 90° + ∠y + 32° = 180°

∠y = 180 - 90° - 32° = 58°

∠y + ∠z + Interior angle of the square = 180° (Sum of angles on a straight line)

58° + ∠z +90° = 180°

∴ ∠z = 32°

∠x = 90°

∠y = 58°

∠z = 32°

24

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."