If wxz = (5x+3), zxy =(8x-4) and wxy is a right angle, find each measure

m∠wxz = 38°

m∠zxy = 52°

Step-by-step explanation:

* Lets explain how to solve the problem

- m∠wxz = (5x + 3)°

- m∠zxy = (8x - 4)°

- ∠wxy is a right angle

∵ xz ray is common between the two angles wxz an zxy

∴ xz ray is between the two rays xw and xy

∴ m∠wxz + m∠zxy = m∠wxy ⇒ (1)

∵ m∠wxz = (5x + 3)°

∵ m∠zxy = (8x - 4)°

∵ ∠wxy is a right angle

∴ m∠wxy = 90°

- Substitute these values in equation (1) above

∴ (5x + 3)° + (8x - 4)° = 90°

- Add like terms

∴ (5x + 8x ) + (3 - 4) = 90

∴ 13x - 1 = 90

- Add 1 to both sides

∴ 13x = 91

- Divide both sides by 13

∴ x = 7

- To find the measure of each angle substitute x by 7

∵ m∠wxz = (5x + 3)°

∴ m∠wxz = 5(7) + 3 = 35 + 3 = 38

∴ m∠wxz = 38°

∵ m∠zxy = (8x - 4)°

∴ m∠zxy = 8(7) - 4 = 56 - 4 = 52

∴ m∠zxy = 52°

Step-by-step explanation:

We know by given

, by definition of right angle.

Also, , by sum of angles.

But, and .

Replacing this equivalences, we have

Now, we use this value to find each angle.

Therefore, the angles are 38° and 52° respectively.

i need more info. are you looked to see there mph? how much they deliver? how far they go?

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."