Question

jl and gk are perpendicular. find the value of x and m∠gkf if the m∠fkl = x + 16 and m∠gkf = 3x + 2.

Explanation:

Step1: Use perpendicular - angle property

Since \(JL\) and \(GK\) are perpendicular, \(\angle GKL = 90^{\circ}\), and \(\angle FKL+\angle GKF=\angle GKL = 90^{\circ}\). So, \((x + 16)+(3x + 2)=90\).

Step2: Simplify the equation

Combine like - terms: \(x+3x+16 + 2=90\), which gives \(4x+18 = 90\).

Step3: Solve for \(x\)

Subtract 18 from both sides: \(4x=90 - 18=72\). Then divide both sides by 4: \(x=\frac{72}{4}=18\).

Step4: Find \(\angle GKF\)

Substitute \(x = 18\) into the expression for \(\angle GKF\). \(\angle GKF=3x + 2=3\times18+2=54 + 2=56^{\circ}\).

Answer:

\(x = 18\), \(m\angle GKF=56^{\circ}\)