Question

lesson 3.6 practice continued for use with pages 190 - 197 find the measure of the indicated angle. 10. ∠1 11. ∠2 12. ∠3 13. ∠4 14. ∠5 15. ∠6

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle1$ and the $60^{\circ}$ angle are vertical angles.

Step2: Determine the measure of $\angle1$

Since vertical angles are equal, $m\angle1 = 60^{\circ}$.

Step3: Identify complementary - angle relationship for $\angle2$

$\angle2$ and the $60^{\circ}$ angle are complementary (sum to $90^{\circ}$).

Step4: Calculate the measure of $\angle2$

$m\angle2=90^{\circ}- 60^{\circ}=30^{\circ}$.

Step5: Identify vertical - angle relationship for $\angle3$

$\angle3$ and $\angle2$ are vertical angles.

Step6: Determine the measure of $\angle3$

Since vertical angles are equal, $m\angle3 = 30^{\circ}$.

Step7: Identify complementary - angle relationship for $\angle4$

$\angle4$ and $\angle3$ are complementary.

Step8: Calculate the measure of $\angle4$

$m\angle4 = 90^{\circ}-30^{\circ}=60^{\circ}$.

Step9: Identify supplementary - angle relationship for $\angle5$

$\angle5$ and the angle adjacent to it (which is $60^{\circ}$) are supplementary (sum to $180^{\circ}$).

Step10: Calculate the measure of $\angle5$

$m\angle5=180^{\circ}-60^{\circ}=120^{\circ}$.

Step11: Identify vertical - angle relationship for $\angle6$

$\angle6$ and $\angle5$ are vertical angles.

Step12: Determine the measure of $\angle6$

Since vertical angles are equal, $m\angle6 = 120^{\circ}$.

Answer:

$m\angle1 = 60^{\circ}$
$m\angle2 = 30^{\circ}$
$m\angle3 = 30^{\circ}$
$m\angle4 = 60^{\circ}$
$m\angle5 = 120^{\circ}$
$m\angle6 = 120^{\circ}$