Question

practice of sec. 2.7

1. find the indicated angles.

<1 =
<2 =
<3 =
<4 =
<5 =

Explanation:

Step1: Vertical - angle property

Vertical angles are equal. $\angle2$ and the $56^{\circ}$ angle are vertical angles, so $\angle2 = 56^{\circ}$.

Step2: Corresponding - angle property

$\angle4$ and the $56^{\circ}$ angle are corresponding angles for parallel lines, so $\angle4=56^{\circ}$.

Step3: Alternate - interior - angle property

$\angle5$ and the $56^{\circ}$ angle are alternate - interior angles for parallel lines, so $\angle5 = 56^{\circ}$.

Step4: Supplementary - angle property

$\angle1$ and $\angle5$ are supplementary (linear pair). Since $\angle5 = 56^{\circ}$, then $\angle1=180^{\circ}-56^{\circ}=124^{\circ}$.

Step5: Vertical - angle property

$\angle3$ and $\angle1$ are vertical angles, so $\angle3 = 124^{\circ}$.

Answer:

$\angle1 = 124^{\circ}$
$\angle2 = 56^{\circ}$
$\angle3 = 124^{\circ}$
$\angle4 = 56^{\circ}$
$\angle5 = 56^{\circ}$