Question

transversal problems with equations (level 1)
score: 2/5 penalty: 1 off
question
given ( m parallel n ), find the value of ( x ).
there is a diagram with two parallel lines ( m ) and ( n ), and a transversal ( t ). the angle on line ( m ) is ( (5x + 5)^circ ) and the angle on line ( n ) is ( (3x + 15)^circ ).
answer attempt 2 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify the angle relationship

Since \( m \parallel n \) and the angles \( (5x + 5)^\circ \) and \( (3x + 15)^\circ \) are alternate interior angles, they are equal. So we set up the equation: \( 5x + 5 = 3x + 15 \)

Step2: Solve for x

Subtract \( 3x \) from both sides: \( 5x - 3x + 5 = 15 \) which simplifies to \( 2x + 5 = 15 \)
Subtract 5 from both sides: \( 2x = 15 - 5 \) so \( 2x = 10 \)
Divide both sides by 2: \( x = \frac{10}{2} = 5 \)

Answer:

\( x = 5 \)