<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 points)
Since <1 and <2 are supplementary angles, their measures sum up to 180 degrees.
Therefore, we have the equation 2y + 12 + 8y + 8 = 180.
Combining like terms, 10y + 20 = 180.
Subtracting 20 from both sides, we get 10y = 160.
Dividing both sides by 10, we find y = 16.
So, m<2 = 8y + 8 = 8(16) + 8 = 128 + 8 = 136 degrees. Therefore, m<2 = 136.
Given that <1 and <2 are supplementary angles, we can write the equation:
m<1 + m<2 = 180
Substituting the given values for m<1 and m<2:
(2y+12) + (8y+8) = 180
Combine like terms:
10y + 20 = 180
Subtract 20 from both sides:
10y = 160
Divide both sides by 10:
y = 16
Now substitute the value of y back into the equation for m<2:
m<2 = 8y + 8 = 8(16) + 8 = 128 + 8 = 136
Therefore, m<2 is 136.
To find the measure of angle <2 (m<2), we need to set up an equation using the information given.
According to the problem, <1 and <2 are supplementary angles, which means they add up to 180 degrees.
So, we have the equation: m<1 + m<2 = 180
Substituting the given values for m<1 and m<2, we have:
(2y + 12) + (8y + 8) = 180
Now, let's simplify and solve for y:
2y + 12 + 8y + 8 = 180
Combining like terms, we have:
10y + 20 = 180
Next, let's isolate the variable by subtracting 20 from both sides of the equation:
10y = 180 - 20
10y = 160
Now, divide both sides of the equation by 10 to solve for y:
y = 160 / 10
y = 16
We have found the value of y as 16.
Now, let's substitute the value of y back into the expression for m<2:
m<2 = 8y + 8
m<2 = 8(16) + 8
m<2 = 128 + 8
m<2 = 136
Therefore, the measure of angle <2 (m<2) is 136 degrees.