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<1 and <2 are supplementary angles. m<1 is 4y + 7, and m<2 is 9y + 4. Find m<2
To find the measure of angle 2 (m<2), we need to use the given information that angle 1 (m<1) and angle 2 are supplementary.
Since the sum of supplementary angles is 180 degrees, we can set up the equation:
m<1 + m<2 = 180
Substituting the given measures:
(4y + 7) + (9y + 4) = 180
Combine like terms:
13y + 11 = 180
Subtract 11 from both sides:
13y = 169
Divide both sides by 13:
y = 13
Now substitute the value of y back into the expression for m<2:
m<2 = 9y + 4
m<2 = 9(13) + 4
m<2 = 117 + 4
m<2 = 121
Therefore, the measure of angle 2 (m<2) is 121 degrees.
To find the measure of angle <2, we need to find the value of y first.
Given that angle <1 and angle <2 are supplementary, their sum is 180 degrees.
So, we can set up the equation:
m<1 + m<2 = 180
Substituting the given values:
(4y + 7) + (9y + 4) = 180
Combining like terms:
13y + 11 = 180
Next, we need to isolate y by subtracting 11 from both sides:
13y = 180 - 11
13y = 169
To solve for y, divide both sides by 13:
y = 169/13
y ≈ 13
Now that we have found the value of y as approximately 13, we can substitute it back into the expression for angle <2 to find its measure:
m<2 = 9y + 4
m<2 = 9(13) + 4
m<2 = 117 + 4
m<2 = 121
Therefore, the measure of angle <2 is 121 degrees.
To find the measure of angle <2, we need to substitute the given values into the equation for angle <2.
Given that <1 and <2 are supplementary angles, we can use the property of supplementary angles: the sum of their measures is 180 degrees.
So, we have the equation:
m<1 + m<2 = 180
Substituting the given values:
(4y + 7) + m<2 = 180
Next, we isolate the variable m<2 by moving the other terms to the other side of the equation:
m<2 = 180 - (4y + 7)
To simplify the right-hand side, we remove the parentheses using the distributive property:
m<2 = 180 - 4y - 7
Combining like terms, we have:
m<2 = 173 - 4y
Therefore, the measure of angle <2 is 173 - 4y.