Question

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

(there is a diagram showing two parallel lines ( m ) and ( n ), and a transversal ( t ) creating angles ( (5x + 5)^circ ) and ( (3x + 15)^circ ) with them.)

answer
( x = ) input box submit answer

Explanation:

Step1: Use the property of alternate interior angles

Since \(m\parallel n\), the angles \((5x + 5)^{\circ}\) and \((3x+15)^{\circ}\) are equal. So we have the equation \(5x + 5=3x + 15\).

Step2: Solve the equation for \(x\)

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

Answer:

\(x = 5\)