Suppose you know that �ÚS and �ÚY are complementary, and that m�ÚS=2(m�ÚY)-30�‹.
Find m�ÚY
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To find the measure of angle �ÚY, we first need to recall the definition of complementary angles. Complementary angles are two angles that add up to 90 degrees.
Given that �ÚS and �ÚY are complementary, we can write the equation:
m�ÚS + m�ÚY = 90 (equation 1)
Next, we are given the information that m�ÚS is equal to 2 times m�ÚY minus 30 degrees. We can express this as an equation as well:
m�ÚS = 2(m�ÚY) - 30 (equation 2)
Since we now have two equations (equation 1 and equation 2) with two unknowns, we can solve this system of equations to find the value of m�ÚY.
First, substitute the value of m�ÚS from equation 2 into equation 1:
2(m�ÚY) - 30 + m�ÚY = 90
Combine like terms:
3(m�ÚY) - 30 = 90
Add 30 to both sides of the equation:
3(m�ÚY) = 120
Divide both sides by 3:
m�ÚY = 40
Therefore, the measure of angle �ÚY is 40 degrees.