Question

when lines intersect, they form congruent angles and supplementary angles. the measure of ∠5 is 110°. find the remaining angle measures. m∠6 =?° m∠7 =?° m∠8 =?°

Explanation:

Step1: Find \(m\angle6\)

Since \(\angle5\) and \(\angle6\) are supplementary (they form a linear pair), we use the formula \(m\angle5 + m\angle6=180^{\circ}\).
Given \(m\angle5 = 110^{\circ}\), then \(m\angle6=180^{\circ}- 110^{\circ}=70^{\circ}\).

Step2: Find \(m\angle7\)

\(\angle5\) and \(\angle7\) are vertical angles. Vertical angles are congruent. So \(m\angle7=m\angle5 = 110^{\circ}\).

Step3: Find \(m\angle8\)

\(\angle6\) and \(\angle8\) are vertical angles. Vertical angles are congruent. So \(m\angle8=m\angle6 = 70^{\circ}\).

Answer:

\(m\angle6 = 70^{\circ}\), \(m\angle7 = 110^{\circ}\), \(m\angle8 = 70^{\circ}\)