Question

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

Answer 1

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°.