Question

∠UVW and ∠XYZ are complementary angles, m∠UVW=(x−10)º , and m∠XYZ=(4x−10)º .

Answer 1

we know that

if ∠UVW and ∠XYZ are complementary angles

then

∠UVW + ∠XYZ=90°

∠UVW=x-10

∠XYZ=4x-10

substitute the values

(x-10)°+(4x-10)°=90°

Solve for x

5x-20=90

5x=90+20

5x=110

x=22°

∠UVW=x-10=22-10=12°

∠XYZ=4x-10=4*22-10=78°

therefore

the answer is

x=22°

∠UVW=12°

∠XYZ=78°

Answer 2

Answer:

m∠UVW = 12°

m∠XYZ =  78°

Step-by-step explanation:

Given:

∠UVW and ∠XYZ are complementary angles.

m∠UVW=(x−10)º , and m∠XYZ=(4x−10)º .

We need to find the measure of each angles.

If the two angles are complementary, then they add upto 90 degrees.

So the sum of two angles must be 90 degrees.

Therefore,

m∠UVW +  m∠XYZ = 90°

(x - 10)° + (4x -10)° = 90°

x - 10 + 4x - 10  = 90

5x - 20 = 90

Add 20 on both sides.

5x - 20 + 20 = 9 0 + 20

5x = 110

Dividing both sides by 5, we get

x = $\frac{110}{5}$

x = 22°

Now plug in x = 22° in m∠UVW and m∠XYZ

m∠UVW = 22 - 10 = 12°

m∠XYZ = 4(22) - 10 = 88 - 10 = 78°

So, m∠UVW = 12° and m∠XYZ =  78°