Question

given ( m parallel n ), find the value of ( x ) and ( y ).

( (6x + 13)^circ )
( y^circ )
( (7x - 5)^circ )

answer attempt 1 out of 2
( x = square )
( y = square )

Explanation:

Step1: Identify vertical angles or linear pairs

Since \( m \parallel n \), the angles \( (6x + 13)^\circ \) and \( (7x - 5)^\circ \) are alternate interior angles? Wait, no, actually, looking at the diagram, \( (6x + 13)^\circ \) and \( (7x - 5)^\circ \) are supplementary? Wait, no, they are adjacent angles forming a linear pair? Wait, no, actually, since \( m \parallel n \), the angle \( (6x + 13)^\circ \) and \( (7x - 5)^\circ \) are same - side? Wait, no, actually, \( (6x + 13)^\circ \) and \( (7x - 5)^\circ \) are adjacent and form a linear pair? Wait, no, let's re - examine. The two angles \( (6x + 13)^\circ \) and \( (7x - 5)^\circ \) are adjacent and form a linear pair? Wait, no, actually, since \( m\parallel n \), the angle \( (6x + 13)^\circ \) and the angle above it (on line \( m \)) are equal. But also, \( (6x + 13)^\circ \) and \( (7x - 5)^\circ \) are supplementary? Wait, no, let's think again.

Wait, the two angles \( (6x + 13)^\circ \) and \( (7x - 5)^\circ \) are adjacent and form a linear pair? No, actually, they are vertical angles? Wait, no, vertical angles are equal. Wait, maybe \( (6x + 13)^\circ=(7x - 5)^\circ \)? Wait, that would be if they are vertical angles. Wait, let's set up the equation:

If \( 6x + 13=7x - 5 \)

Step2: Solve for x

Subtract \( 6x \) from both sides:

\( 6x+13 - 6x=7x - 5-6x \)

\( 13=x - 5 \)

Add 5 to both sides:

\( 13 + 5=x-5 + 5 \)

\( x = 18 \)

Step3: Find the measure of the angle

Now, substitute \( x = 18 \) into \( 6x+13 \):

\( 6\times18+13=108 + 13=121^\circ \)

Substitute \( x = 18 \) into \( 7x-5 \):

\( 7\times18-5=126 - 5 = 121^\circ \)

Now, the angle \( y^\circ \) and \( (7x - 5)^\circ \) are supplementary (since they form a linear pair). So \( y+(7x - 5)=180 \)

Substitute \( x = 18 \), \( 7x-5 = 121 \)

So \( y+121 = 180 \)

Step4: Solve for y

Subtract 121 from both sides:

\( y=180 - 121=59 \)

Answer:

\( x = 18 \), \( y = 59 \)