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.

75

step-by-step explanation:

you do x-29=46 (the number of cantaloupes sold)

in order to find x, you have to find what minus 29 equals 46, meaning you'd have to add 29 to 46.

29+46=75

if you replace x with 75, the equation looks like:

75-29=46

x=75