Question

name: ____________ unit 3: parallel & perpendicular lines date: __________ bell: __ homework 2: angles & parallel lines this is a 2 - page document 1. if m∠8 = 23°, find the measure of each missing angle. give your reasoning. a. m∠1 = b. m∠2 = c. m∠3 = d. m∠4 = e. m∠5 = f. m∠6 = g. m∠7 = 2. if m∠9 = 97° and m∠12 = 114°, find the measure of each missing angle. a. m∠1 = f. m∠6 = k. m∠13 = b. m∠2 = g. m∠7 = l. m∠14 = c. m∠3 = h. m∠8 = m. m∠15 = d. m∠4 = i. m∠10 = n. m∠16 = e. m∠5 = j. m∠11 = 3. if m∠2 = 50°, m∠3 = 27° and m∠8 = 70°, find the measure of each missing angle. a. m∠1 = d. m∠6 = g. m∠10 = b. m∠4 = e. m∠7 = c. m∠5 = f. m∠9 = 4. if m∠3 = 54°, find the measure of each missing angle. a. m∠1 = f. m∠7 = k. m∠12 = b. m∠2 = g. m∠8 = l. m∠13 = c. m∠4 = h. m∠9 = m. m∠14 = d. m∠5 = i. m∠10 =

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. If $\angle8 = 23^{\circ}$, then $\angle3=\angle8 = 23^{\circ}$ (vertical angles).

Step2: Identify corresponding - angle relationship

Corresponding angles are equal when lines are parallel. $\angle1=\angle8 = 23^{\circ}$ (corresponding angles).

Step3: Identify alternate - interior - angle relationship

Alternate - interior angles are equal when lines are parallel. $\angle5=\angle8 = 23^{\circ}$ (alternate - interior angles).

Step4: Identify linear - pair relationship

A linear pair of angles sums to $180^{\circ}$. $\angle2 = 180^{\circ}-\angle1=180 - 23=157^{\circ}$ (linear - pair with $\angle1$). $\angle4 = 180^{\circ}-\angle3=180 - 23 = 157^{\circ}$ (linear - pair with $\angle3$). $\angle6=180^{\circ}-\angle5 = 157^{\circ}$ (linear - pair with $\angle5$). $\angle7=\angle2 = 157^{\circ}$ (vertical angles with $\angle2$).

Answer:

a. $23^{\circ}$
b. $157^{\circ}$
c. $23^{\circ}$
d. $157^{\circ}$
e. $23^{\circ}$
f. $157^{\circ}$
g. $157^{\circ}$