Let's analyze the given quadrilateral so that we can find the measure of ∠ZYW.
First, we must find the value of x. By the definition of a rectangle, we know that WXYZ has four right angles. Therefore, the measure of m ∠XYZ is 90.
m ∠XYZ= 90
With the Angle Addition Postulate we can express m ∠XYZ as a sum of m ∠ZYW and m ∠WYX. Since ∠XYZ is a right angle and its measure is 90, this means that ∠ZYW and ∠WYX are complementary angles.
m ∠ZYW + m ∠WYX = m ∠XYZ
⇕
m ∠ZYW + m ∠WYX = 90
We are given that m ∠ZYW= 2x-7 and m ∠WYX= 2x+5. We will substitute these expressions into our equation.
2x-7 + 2x+5 = 90
Let's solve it!
