Question

find the measure of ∠rtn. (55 - 2x)° (63 - 6x)° m∠rtn = ° submit work it out not feeling ready yet? these can help: transversals of parallel lines: find angle measures (81) solve linear equations: mixed review (81) lesson: transversals of parallel lines

Explanation:

Step1: Assume parallel lines

Assume lines \(PO\) and \(RQ\) are parallel, and \(MN\) is a transversal. Then \((55 - 2x)^{\circ}\) and \((63 - 6x)^{\circ}\) are corresponding - angles.
\[55 - 2x=63 - 6x\]

Step2: Solve for \(x\)

Add \(6x\) to both sides: \(55 - 2x+6x=63 - 6x+6x\), which simplifies to \(55 + 4x=63\).
Subtract 55 from both sides: \(4x=63 - 55\), so \(4x = 8\).
Divide both sides by 4: \(x = 2\).

Step3: Find \(\angle RTN\)

Substitute \(x = 2\) into the expression for \(\angle RTN=(63 - 6x)^{\circ}\).
\(\angle RTN=63-6\times2=63 - 12=51^{\circ}\)

Answer:

\(51\)