Enter your answer and show all the steps that you use to solve this problem in the space provided. ∠1 and ∠2 are supplementary angles. m∠1 is 4y+7 , and m∠2 is 9y+4 . Find m∠2 .
Since ∠1 and ∠2 are supplementary angles, their measures add up to 180 degrees.
So, we can write the equation:
m∠1 + m∠2 = 180
Substituting the given measures into the equation, we have:
4y + 7 + 9y + 4 = 180
Combining like terms, we have:
13y + 11 = 180
Next, we isolate the variable term by subtracting 11 from both sides:
13y = 180 - 11
13y = 169
Finally, we solve for y by dividing both sides by 13:
y = 169/13
Therefore, we find that y = 13.
To find m∠2, we substitute the value of y back into the expression for ∠2:
m∠2 = 9y + 4
m∠2 = 9(13) + 4
m∠2 = 117 + 4
m∠2 = 121
Hence, m∠2 is 121 degrees.
To find the measure of ∠2 (m∠2), we will set up an equation based on the given information and solve for y.
Given:
∠1 and ∠2 are supplementary angles, which means the sum of their measures is 180 degrees.
m∠1 = 4y + 7
m∠2 = 9y + 4
Since ∠1 and ∠2 are supplementary, we have the equation:
m∠1 + m∠2 = 180
Substituting the given values:
(4y + 7) + (9y + 4) = 180
Combining like terms:
4y + 7 + 9y + 4 = 180
13y + 11 = 180
Subtract 11 from both sides of the equation:
13y = 180 - 11
13y = 169
Divide both sides by 13 to isolate y:
y = 169 ÷ 13
y ≈ 13
Now that we have found the value of y, we can substitute it into the equation for m∠2:
m∠2 = 9y + 4
m∠2 = 9(13) + 4
m∠2 = 117 + 4
m∠2 = 121
Therefore, the measure of ∠2 (m∠2) is 121 degrees.
To find the measure of ∠2 (m∠2), we need to equate it to the value of 9y + 4.
Given that ∠1 and ∠2 are supplementary angles, we have the following equation:
m∠1 + m∠2 = 180
Substituting the given values:
4y + 7 + 9y + 4 = 180
Combining like terms:
13y + 11 = 180
To isolate the variable, we subtract 11 from both sides of the equation:
13y = 180 - 11
Simplifying:
13y = 169
Finally, to find the value of y, we divide both sides of the equation by 13:
y = 169/13
Therefore, the value of y is 13.
To find m∠2, we substitute the value of y back into the equation:
m∠2 = 9y + 4
m∠2 = 9(13) + 4
Simplifying:
m∠2 = 117 + 4
m∠2 = 121
Hence, the measure of ∠2 (m∠2) is 121.