Problem 11
Answer: Angle C and angle F
Explanation: Angle C and the 80 degree angle are vertical angles. Vertical angles are always congruent. Angle F is equal to angle C because they are alternate interior angles.
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Problem 12
Answer: 100 degrees
Explanation: Solve the equation E+F = 180, where F = 80 found earlier above. You should get E = 100.
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Problem 13
Answer: 80 degrees
Explanation: This was mentioned earlier in problem 11.
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Problem 14
Answers: complement = 50, supplement = 140
Explanation: Complementary angles always add to 90. Supplementary angles always add to 180. An example of supplementary angles are angles E and F forming a straight line angle.
You need two pieces and 1 has to be 2x longer than the other
set x as the smaller piece (easier to always go with the smaller value as x)
the other piece is 2x (double in size)
your equations would be 3x=240>>> x= 60
so smaller piece/ x= 60
bigger piece/ 2x= 120
Answer:

Step-by-step explanation:
We want to solve
, where
.
We rewrite in terms of sine and cosine.


Use the Pythagorean identity:
.




This is a quadratic equation in
.
By the quadratic formula, we have:




or 
or 
or 
When
, 
on the interval
.
When
,
is not defined because 
1 ft = 12 inches
so 2 ft = (2 * 12) = 24 inches
and 1/4 ft = 1/4 * 12 = 12/4 = 3 inches
for a total of 27 inches
X= -4y let this be equation 1
x+5y=2 let this be equation 2
substitute equation 1 in 2
-4y + 5y = 2
y=2
substitute the value of y in equation 1
x= -4y
x= -4(2)
x= -8