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!
