Question

1. if m < 8 = 23°, find the measure of each missing angle. state the angle type.

day 7: transversals with algebra
per

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle 8$ and $\angle 6$ are vertical angles, so $m\angle6 = m\angle8=23^{\circ}$.

Step2: Identify corresponding - angle relationship

Corresponding angles are equal. $\angle 6$ and $\angle 2$ are corresponding angles, so $m\angle2 = m\angle6 = 23^{\circ}$. $\angle 8$ and $\angle 4$ are corresponding angles, so $m\angle4=m\angle8 = 23^{\circ}$.

Step3: Identify alternate - interior and alternate - exterior angle relationships

Alternate - interior angles are equal. $\angle 6$ and $\angle 4$ are alternate - interior angles. Alternate - exterior angles are equal. $\angle 8$ and $\angle 2$ are alternate - exterior angles.

Step4: Use linear - pair relationship

A linear pair of angles is supplementary (sum to $180^{\circ}$). $\angle 1$ and $\angle 2$ form a linear pair. So $m\angle1=180 - m\angle2=180 - 23=157^{\circ}$. Similarly, $\angle 3$ and $\angle 2$ are vertical angles, so $m\angle3 = m\angle1 = 157^{\circ}$. $\angle 5$ and $\angle 4$ form a linear pair, so $m\angle5=180 - m\angle4 = 157^{\circ}$. $\angle 7$ and $\angle 8$ form a linear pair, so $m\angle7=180 - m\angle8 = 157^{\circ}$.

Answer:

a. $m\angle1 = 157^{\circ}$, linear - pair to $\angle2$
b. $m\angle2 = 23^{\circ}$, vertical to $\angle6$ and corresponding to $\angle6$
c. $m\angle3 = 157^{\circ}$, vertical to $\angle1$
d. $m\angle4 = 23^{\circ}$, vertical to $\angle6$ and corresponding to $\angle8$
e. $m\angle5 = 157^{\circ}$, linear - pair to $\angle4$
f. $m\angle6 = 23^{\circ}$, vertical to $\angle8$
g. $m\angle7 = 157^{\circ}$, linear - pair to $\angle8$