Question

find the values of x and y.
(7y)°
(4x - 11)°
43°
84°
x =
y =

Explanation:

Step1: Set up an equation for the angle involving \(x\)

We know that \((4x - 11)+43 = 84\) since the sum of two adjacent - angles \(\angle KNL\) and \(\angle LNM\) equals \(\angle KNM\).
\[4x-11 + 43=84\]
\[4x+32 = 84\]

Step2: Solve the equation for \(x\)

Subtract 32 from both sides:
\[4x=84 - 32\]
\[4x=52\]
Divide both sides by 4:
\[x=\frac{52}{4}=13\]

Step3: Set up an equation for the angle involving \(y\)

We know that \(7y+84 = 90\) since \(\angle JNK\) and \(\angle KNM\) are complementary (the right - angle at \(N\) is \(90^{\circ}\)).
\[7y=90 - 84\]
\[7y = 6\]

Step4: Solve the equation for \(y\)

\[y=\frac{6}{7}\]

Answer:

\(x = 13\)
\(y=\frac{6}{7}\)