Let's analyze the given rectangle so that we can find m∠ EFD.
By the definition of a rectangle, we know that DEFG has four right angles. Therefore, the measure of m ∠ EFG is 90.
m ∠ EFG= 90
With the Angle Addition Postulate we can express m ∠ EFG as a sum of m ∠ EFD and m ∠ DFG.
m ∠ EFD + m ∠ DFG = m ∠ EFG
⇕
m ∠ EFD + m ∠ DFG = 90
We are given that m ∠ EFD= 2x-3 and m ∠ DFG= x+12, and we have been asked to find the measure of ∠ EFD. We will first substitute these expressions into our equation for m∠ EFG to find the value of x. Then we can substitute the value of x into the equation of m∠ EFD to find its measure.
2x-3 + x+12 = 90
Let's solve it!
