Question

the measure of $angle 5$ is $110^\circ$. find the remaining angle measures.$m\angle 6 =LXB0m\angle 8 =$look for pairs of vertical angles and supplementary angles to find the missing measures.

Explanation:

Step1: Find m∠6 (supplementary to ∠5)

∠5 and ∠6 are supplementary, so $m\angle6 = 180^\circ - m\angle5 = 180^\circ - 110^\circ$

Step2: Find m∠7 (vertical to ∠6)

∠7 and ∠6 are vertical angles, so $m\angle7 = m\angle6$

Step3: Find m∠8 (vertical to ∠5)

∠8 and ∠5 are vertical angles, so $m\angle8 = m\angle5$

Answer:

$m\angle6 = 70^\circ$
$m\angle7 = 70^\circ$
$m\angle8 = 110^\circ$