Question

given ( m parallel n ), find the value of ( x ). ((3x - 23)^circ) ((7x - 7)^circ) answer attempt 2 out of 2 ( x = ) submit answer

Explanation:

Step1: Identify angle relationship

Since \( m \parallel n \), the two angles \( (3x - 23)^\circ \) and \( (7x - 7)^\circ \) are same - side exterior angles? Wait, no, actually, when two parallel lines are cut by a transversal, same - side interior angles are supplementary, but here these two angles are actually same - side exterior angles? Wait, no, let's look at the positions. Wait, the angle \( (3x - 23)^\circ \) and the angle \( (7x - 7)^\circ \): when \( m\parallel n \), the sum of these two angles should be \( 180^\circ \) because they are same - side exterior angles (or we can think of them as consecutive exterior angles). So we set up the equation:
\( (3x - 23)+(7x - 7)=180 \)

Step2: Simplify the equation

First, combine like terms:
\( 3x+7x-23 - 7=180 \)
\( 10x-30 = 180 \)

Step3: Solve for x

Add 30 to both sides of the equation:
\( 10x-30 + 30=180 + 30 \)
\( 10x=210 \)
Then divide both sides by 10:
\( x=\frac{210}{10}=21 \)

Answer:

\( 21 \)