Question

example 2 find unknown angle measures in the figure, a || b. what are the measures of ∠4 and ∠5? explain. use what you know about the angles created when parallel lines are cut by a transversal. m∠4 = 99° the 99° angle and ∠4 are corresponding angles. m∠4 + m∠5 = 180° ∠4 and ∠5 are supplementary angles. m∠5 = 180° − 99° m∠5 = 81° try it! what are the measures of ∠7 and ∠2? explain

Explanation:

Step1: Identify ∠1's relationship

From the figure, ∠1 corresponds to the 99° angle (since \(a \parallel b\), corresponding angles are congruent).
\(m\angle1 = 99^\circ\)

Step2: Identify ∠2's relationship

∠2 and ∠1 are supplementary (they form a linear pair, summing to \(180^\circ\)).
\(m\angle2 = 180^\circ - m\angle1\)

Step3: Calculate ∠2's measure

Substitute \(m\angle1 = 99^\circ\) into the formula.
\(m\angle2 = 180^\circ - 99^\circ = 81^\circ\)

Answer:

\(m\angle1 = 99^\circ\), \(m\angle2 = 81^\circ\)
∠1 is congruent to the given 99° corresponding angle (due to parallel lines cut by a transversal), and ∠2 is supplementary to ∠1, so it equals \(180^\circ - 99^\circ = 81^\circ\).