Question

in the figure, p || q with m∠1 = 6x + 39 and m∠2 = 10x - 3, first find x and then find m∠2. what is the relationship of ∠1 and ∠2? which equation should you use to solve? x = 10.5 m∠2 = consecutive exterior angles consecutive interior angles alternate exterior angles alternate interior angles vertical angles linear pair corresponding angles

Explanation:

Step1: Identify the relationship between ∠1 and ∠2

Since \(p\parallel q\), ∠1 and ∠2 are alternate exterior angles. Alternate exterior angles are equal when two parallel lines are cut by a transversal.

Step2: Set up the equation

We know that \(m\angle1 = 6x + 39\) and \(m\angle2=10x - 3\). Because \(m\angle1=m\angle2\) (alternate exterior angles), we have the equation \(6x + 39=10x - 3\).

Step3: Solve for \(x\)

Subtract \(6x\) from both sides: \(39 = 4x- 3\).
Add 3 to both sides: \(42 = 4x\).
Divide both sides by 4: \(x=\frac{42}{4}=10.5\).

Step4: Find \(m\angle2\)

Substitute \(x = 10.5\) into the expression for \(m\angle2\).
\(m\angle2=10x - 3\), so \(m\angle2=10\times10.5-3\).
\(m\angle2 = 105 - 3=102^{\circ}\).

Answer:

\(x = 10.5\), \(m\angle2=102^{\circ}\)