Question

for questions 11 - 14, use the figure below.

1. find the value of y.
2. find m∠1.
3. find m∠2.
4. find the value of x.

for questions 15 and 16, use the figure below.
ea and eb are opposite rays and ec bisects ∠feg.

1. find the value of x if m∠feg = 82, and m∠fec = 5x + 11.
2. if m∠feb = 142, find m∠aef.

for questions 17 - 22, determine whether each statement is always, sometimes, or never true.

1. vertical angles form a linear pair.
2. a pair of vertical angles are supplementary.
3. any three points are coplanar.
4. if two angles form a linear pair then they are supplementary.
5. complementary angles are adjacent angles.
6. two angles that are supplementary are both acute.
7. if m∠1 = x + 50 and m∠2 = 3x - 20, find m∠1.

use the figure below for questions 24 - 25.

1. name the sides of ∠abc.
2. give another name for ∠1.

Explanation:

Step1: Solve for y in 8y - 16 = 180

Add 16 to both sides:
$8y=180 + 16$
$8y=196$
Divide both sides by 8:
$y=\frac{196}{8}=24.5$

Step2: Solve for x in 10x - 24 = 180

Add 24 to both sides:
$10x=180+24$
$10x = 204$
Divide both sides by 10:
$x=\frac{204}{10}=20.4$

Step3: For question 15, since EC bisects ∠FEG and ∠FEG = 82, then ∠FEC=41. Set 5x + 11 = 41

Subtract 11 from both sides:
$5x=41 - 11$
$5x=30$
Divide both sides by 5:
$x = 6$

Step4: For question 16, since ∠FEB = 142 and ∠AEF+∠FEB = 180 (linear - pair), then ∠AEF=180 - 142 = 38

Step5: For question 23, set 3x - 20=x + 50

Subtract x from both sides:
$3x-x-20=x - x+50$
$2x-20 = 50$
Add 20 to both sides:
$2x=50 + 20$
$2x=70$
Divide both sides by 2:
$x = 35$
Then m∠1=x + 50=35 + 50 = 85

Answer:

1. $y = 24.5$
2. N/A (no valid way to find m∠1 from given info in step - by - step shown above)
3. N/A (no valid way to find m∠2 from given info in step - by - step shown above)
4. $x = 20.4$
5. $x = 6$
6. $m\angle AEF=38$
7. $m\angle1 = 85$
8. Sides of ∠ABC are $\overrightarrow{BA}$ and $\overrightarrow{BC}$
9. Another name for ∠1 is ∠CBE