Question

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

y =

Explanation:

Step1: Set up equation for angle - sum

We know that the sum of the angles \((4x - 11)^{\circ}\) and \(43^{\circ}\) is \(84^{\circ}\). So, \((4x-11)+43 = 84\).

Step2: Simplify the left - hand side

Combine like terms: \(4x+( - 11 + 43)=84\), which gives \(4x + 32=84\).

Step3: Solve for \(x\)

Subtract 32 from both sides: \(4x=84 - 32\), so \(4x = 52\). Then divide both sides by 4: \(x=\frac{52}{4}=13\).

Step4: Set up equation for the other angle

We know that \((7y)^{\circ}\) and \(84^{\circ}\) are complementary (since \(\angle JNM\) is a right - angle, \(90^{\circ}\)). So, \(7y+84 = 90\).

Step5: Solve for \(y\)

Subtract 84 from both sides: \(7y=90 - 84\), so \(7y = 6\). Then \(y=\frac{6}{7}\).

Answer:

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