Question

1. two parallel lines are cut by a transversal. suppose $\angle 1$ and $\angle 2$ are consecutive interior angles and that $m\angle 1 = (16x + 13)^\circ$ and $m\angle 2 = (7x + 6)^\circ$ what is $m\angle 2$? round to a whole number.

Explanation:

Step1: Recall consecutive interior angles property

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary, so \(m\angle1 + m\angle2 = 180^\circ\).
Substitute \(m\angle1=(16x + 13)^\circ\) and \(m\angle2=(7x + 6)^\circ\) into the equation: \((16x + 13)+(7x + 6)=180\).

Step2: Solve for \(x\)

Combine like terms: \(16x+7x + 13 + 6 = 180\) → \(23x+19 = 180\).
Subtract 19 from both sides: \(23x=180 - 19=161\).
Divide both sides by 23: \(x=\frac{161}{23}=7\).

Step3: Calculate \(m\angle2\)

Substitute \(x = 7\) into \(m\angle2=(7x + 6)^\circ\): \(m\angle2=(7\times7 + 6)^\circ=(49 + 6)^\circ = 55^\circ\).

Answer:

\(55^\circ\)