Question

the measure of ∠5 is 110°. find the remaining angle measures. m∠6 = m∠7 = m∠8 =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle5$ and $\angle7$ are vertical angles. So $m\angle7 = m\angle5=110^{\circ}$.

Step2: Use linear - pair property

$\angle5$ and $\angle6$ form a linear - pair. A linear - pair of angles is supplementary, so $m\angle5 + m\angle6=180^{\circ}$. Then $m\angle6 = 180 - m\angle5=180 - 110=70^{\circ}$.

Step3: Use vertical - angle property again

$\angle6$ and $\angle8$ are vertical angles. So $m\angle8 = m\angle6 = 70^{\circ}$.

Answer:

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