Answer:
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°
Answer:
Step-by-step explanation:
We know by given
[tex]\angle WXY = 90\°[/tex], by definition of right angle.
Also, [tex]\angle WXZ + \angle ZXY = \angle WXY[/tex], by sum of angles.
But, [tex]\angle WXZ=5x+3[/tex] and [tex]\angle ZXY = 8x-4[/tex].
Replacing this equivalences, we have
[tex]5x+3+8x-4=90\\13x-1=90\\13x=91\\x=\frac{91}{13}\\ x=7[/tex]
Now, we use this value to find each angle.
[tex]\angle WXZ = 5x+3=5(7)+3=35+3=38\°\\\angle ZXY = 8x-4=8(7)-4=56-4=52\°[/tex]
Therefore, the angles are 38° and 52° respectively.
