Question

find the measure of ∠rtn.
m∠rtn = □°
submit

Explanation:

Step1: Identify parallel lines and transversal

Lines \( RQ \) and \( PO \) are parallel, and \( NW \) is a transversal. So, the alternate interior angles \( \angle RTM \) (wait, actually the angles \( (63 - 6x)^\circ \) and \( (55 - 2x)^\circ \) should be equal? Wait, no, maybe they are same - side? Wait, no, looking at the diagram, since \( RQ \parallel PO \), the angles \( (63 - 6x)^\circ \) and \( (55 - 2x)^\circ \) are same - side interior angles? Wait, no, maybe they are equal? Wait, no, let's think again. Wait, the two angles \( (63 - 6x)^\circ \) and \( (55 - 2x)^\circ \): since \( RQ \parallel PO \), and \( NW \) is a transversal, maybe these two angles are equal? Wait, no, maybe they are supplementary? Wait, no, let's check the diagram. Wait, the lines \( RQ \) and \( PO \) are parallel, and \( NW \) is a transversal. So the angle at \( T \) on line \( RQ \) is \( (63 - 6x)^\circ \) and the angle at \( S \) on line \( PO \) is \( (55 - 2x)^\circ \). Since \( RQ \parallel PO \), these two angles should be equal (alternate interior angles). So we set up the equation:
\( 63 - 6x=55 - 2x \)

Step2: Solve for \( x \)

Subtract \( 55 \) from both sides:
\( 63 - 55-6x=55 - 55-2x \)
\( 8 - 6x=- 2x \)
Add \( 6x \) to both sides:
\( 8-6x + 6x=-2x + 6x \)
\( 8 = 4x \)
Divide both sides by \( 4 \):
\( x=\frac{8}{4}=2 \)

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

Now substitute \( x = 2 \) into the expression for \( \angle RTW \), which is \( (63 - 6x)^\circ \)
\( 63-6\times2=63 - 12 = 51 \)

Answer:

\( 51 \)