Question

calculator
in this diagram, parallel lines are cut by transversal.
given: ( mangle1=(5x + 38)^{circ} ) and ( mangle6=(7x + 10)^{circ} )
what is the value of ( x )?
( x=)

Explanation:

Step1: Use the property of alternate interior angles

When parallel lines are cut by a transversal, \(\angle1\) and \(\angle6\) are alternate interior angles. So \(m\angle1 = m\angle6\).

$$5x + 38=7x + 10$$

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides:

$$38 = 2x+10$$

Subtract \(10\) from both sides:

$$28 = 2x$$

Divide both sides by \(2\):

$$x = 14$$

Answer:

\(14\)