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y = 90°

Solution:

The reference image for the answer is attached below.

The sum of opposite interior angles is equal to the exterior angles.

m∠BAC + m∠ACB = 110°

m∠BAC + 70° = 110°

m∠BAC = 110° –  70°

m∠BAC = 40°

m∠BAD + m∠DAC = 40°

x + x = 40°

2x = 40°

Divide by 2 on both sides of the equation.

x = 20°

In triangle DAC,

Sum of all the angles of a triangle = 180°

m∠DAC + m∠ACD + m∠CDA = 180°

20° + 70° + m∠CDA = 180°

90° + m∠CDA = 180°

m∠CDA = 180° – 90°

m∠CDA = 90°

∠CDA and y lies on the straight line. So they form a linear pair.

y + m∠CDA = 180°

y + 90° = 180°

y = 180° – 90°

y = 90°

The value of y is 90°.

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.

- "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."