Question

find the measures of the indicated angles, using the diagram below. a=(14x + 16)° and g=(7x - 4)°, find the measures of a and g.

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), \(\angle A\) and \(\angle G\) are corresponding angles, so \(\angle A=\angle G\).
Set up the equation \(14x + 16=7x-4\).

Step2: Solve the equation for \(x\)

Subtract \(7x\) from both sides: \(14x-7x + 16=7x-7x - 4\), which simplifies to \(7x+16=-4\).
Then subtract 16 from both sides: \(7x+16 - 16=-4 - 16\), getting \(7x=-20\).
Divide both sides by 7: \(x =-\frac{20}{7}\). This is incorrect. Let's assume they are supplementary (adjacent - exterior or adjacent - interior). If they are supplementary, \(A + G=180^{\circ}\).
Set up the equation \((14x + 16)+(7x-4)=180\).
Combine like - terms: \(14x+7x+16 - 4=180\), so \(21x + 12=180\).
Subtract 12 from both sides: \(21x+12 - 12=180 - 12\), getting \(21x=168\).
Divide both sides by 21: \(x = 8\).

Step3: Find the measure of \(\angle A\)

Substitute \(x = 8\) into the expression for \(A\): \(A=14x + 16=14\times8+16=112 + 16=128^{\circ}\).

Step4: Find the measure of \(\angle G\)

Substitute \(x = 8\) into the expression for \(G\): \(G=7x-4=7\times8-4=56 - 4=52^{\circ}\).

Answer:

\(A = 128^{\circ}\)
\(G = 52^{\circ}\)