Question

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

Answer 1

The angles are 38° and 52° respectively.

Explanation:

We know by given

`\angle WXY = 90\°`, by definition of right angle.

Also,
`\angle WXZ + \angle ZXY = \angle WXY`, by sum of angles.

But,
`\angle WXZ=5x+3` and
`\angle ZXY = 8x-4`.

Replacing this equivalences, we have

`5x+3+8x-4=90\\13x-1=90\\13x=91\\x=(91)/(13)\\ x=7`

Now, we use this value to find each angle.

`\angle WXZ = 5x+3=5(7)+3=35+3=38\°\\\angle ZXY = 8x-4=8(7)-4=56-4=52\°`

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

Answer 2

m∠wxz = 38°

m∠zxy = 52°

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°