Question

1. if ( mangle8 = 23^{circ} ), find the measure of each missing angle. give your reasoning.

a. ( mangle1=)
b. ( mangle2=)
c. ( mangle3=)
d. ( mangle4=)
e. ( mangle5=)
f. ( mangle6=)
g. ( mangle7=)

Explanation:

Step1: Vertical angles

Vertical angles are equal. $\angle8$ and $\angle6$ are vertical angles. So $m\angle6 = 23^{\circ}$.

Step2: Linear - pair (supplementary angles)

$\angle8$ and $\angle5$ form a linear - pair. Since the sum of angles in a linear - pair is $180^{\circ}$, $m\angle5=180^{\circ}-m\angle8 = 180 - 23=157^{\circ}$.
$\angle5$ and $\angle7$ are vertical angles. So $m\angle7 = 157^{\circ}$.

Step3: Corresponding angles

Assume the two horizontal lines are parallel. $\angle2$ and $\angle6$ are corresponding angles. So $m\angle2 = 23^{\circ}$.

Step4: Linear - pair (supplementary angles)

$\angle1$ and $\angle2$ form a linear - pair. So $m\angle1=180^{\circ}-m\angle2 = 180 - 23 = 157^{\circ}$.
$\angle1$ and $\angle3$ are vertical angles. So $m\angle3 = 157^{\circ}$.
$\angle2$ and $\angle4$ are vertical angles. So $m\angle4 = 23^{\circ}$.

Answer:

a. $m\angle1 = 157^{\circ}$
b. $m\angle2 = 23^{\circ}$
c. $m\angle3 = 157^{\circ}$
d. $m\angle4 = 23^{\circ}$
e. $m\angle5 = 157^{\circ}$
f. $m\angle6 = 23^{\circ}$
g. $m\angle7 = 157^{\circ}$