Question

applying the definition of a square
mnop is a square. what are the values of t and f?
( t = )
( f = )

Explanation:

Step1: Use the property of a square's angles

All angles in a square are \(90^{\circ}\). So, for \(\angle M=(4t + 20)^{\circ}\), we set up the equation \(4t+20 = 90\).
Subtract \(20\) from both sides: \(4t=90 - 20\), which simplifies to \(4t = 70\).
Divide both sides by \(4\): \(t=\frac{70}{4}=17.5\).

Step2: Solve for \(f\)

For \(\angle N=(7f + 6)^{\circ}\), set up the equation \(7f+6 = 90\).
Subtract \(6\) from both sides: \(7f=90 - 6\), which simplifies to \(7f = 84\).
Divide both sides by \(7\): \(f=\frac{84}{7}=12\).

Answer:

\(t = 17.5\), \(f = 12\)