Question

I have three hours!!!!!!!!!!!

1.
<1 and <2 are supplementary angles. m<1 is 2y+12 and the m<2 is 8y+8. Find m<2. You must show all steps and work in order to receive full credit.


2.
If line n bisects CE¯¯¯¯¯¯¯¯
, Find CD. You must show all your work in order to receive full credit.

Answer 1

Explanation:

FOR QUESTION#1

the answer is m<2=136

given:

2y+12

8y+8

supplementary means 180.

(2y+12)+(8y+8)=180

2y+12+8y+8=180

add

10y+20=180

sub 20 from each side

10y=160

divide by 10

y=16

plug back into m<2 equation.

8(16)+8

m<2=136

your welcome!

Answer 2

1. To find the measure of angle <2, which is denoted as m<2, we need to use the fact that angles 1 and 2 are supplementary.

Supplementary angles add up to 180 degrees. So, we can write an equation:

m<1 + m<2 = 180

Given that m<1 = 2y + 12, we can substitute this expression into the equation:

(2y + 12) + m<2 = 180

Next, we can simplify the equation by combining like terms:

2y + m<2 + 12 = 180

Now, let's isolate m<2 by subtracting 12 from both sides:

2y + m<2 = 180 - 12

2y + m<2 = 168

To find m<2, we need to isolate the m<2 term by subtracting 2y from both sides:

m<2 = 168 - 2y

So, the measure of angle <2, denoted as m<2, is 168 - 2y.

2. Given that line n bisects segment CE, we know that CD is the same length as DE.

The given equation CE = 5(x - 3) represents the length of CE in terms of x.

Since CD and DE are equal, we can set up an equation:

CD = DE

To find the length of CD, we need to determine the length of DE.

Since CE = CD + DE, we can substitute the given expression for CE:

5(x - 3) = CD + DE

Since CD and DE are equal, we can replace DE with CD in the equation:

5(x - 3) = CD + CD

Simplifying the equation, we get:

5(x - 3) = 2CD

Now, we can solve for CD by dividing both sides of the equation by 2:

CD = (5(x - 3)) / 2

So, the length of CD is (5(x - 3)) / 2.

Explanation:

Have a good day <3