m∠WYX = (2x-1) ° and m∠WYZ = (4x+1) °. If ∠WYX and ∠WYZ are complementary, what is the measure of each angle?

We are given : m∠WYX = (2x-1) ° and m∠WYZ = (4x+1) °.

∠WYX and ∠WYZ are complementary.

We know, sum of complementary angles is = 90°.

So, we need to add ∠WYX and ∠WYZ and set it equal to 90°.

m∠WYX + m∠WYZ = 90°.

Plugging values of ∠WYX and ∠WYZ in the above equation, we get

(2x-1) ° + (4x+1) ° = 90°.

Removing parentheses from both sides,

2x-1 + 4x+1 = 90.

Combining like terms,

2x+4x = 6x and - 1+1 = 0

6x + 0 = 90.

6x=90.

Dividing both sides by 6.

6x/6 = 90/6

x = 15.

Plugging value of x=15.

m∠WYX = (2x-1) ° = 2*15 - 1 = 30 - 1 = 29

m∠WYZ = (4x+1) ° = 4*15 + 1 = 60+1 = 61.

Therefore, ∠WYX=29° and ∠WYZ=61°.