Question

find the values of x and y.

x =

y =

Explanation:

Step1: Find the value of \(x\)

Since \(\angle DKF = 90^{\circ}\), we have \(42^{\circ}+12x^{\circ}=90^{\circ}\).
Subtract \(42^{\circ}\) from both sides: \(12x = 90 - 42\).
So, \(12x=48\).
Divide both sides by \(12\): \(x=\frac{48}{12}\).

Step2: Find the value of \(y\)

Vertical angles are equal. \(\angle HKG = 42^{\circ}\), and \(\angle HKG\) and \(6y^{\circ}\) are complementary to the right - angle at \(K\) (alternatively, using vertical angle and complementary angle relationships). Since \(\angle HKG = 42^{\circ}\) and \(6y^{\circ}\) forms a right - angle with \(\angle HKG\) (or using vertical angle equivalence in the right - angle split).
We know that \(6y = 48\) (because the non - right angles in the right - angle split are equal in pairs).
Divide both sides by \(6\): \(y=\frac{48}{6}\).

Answer:

\(x = 4\), \(y = 8\)