Question 421876: The measure of angle t is 35º greater than 4 times the measure of its supplement Found 2 solutions by algebrahouse.com, Gogonati:Answer by algebrahouse.com(1659) (Show Source):
t = measure of angle t
180 - t = measure of supplement {supplementary angles add up to 180}
t = 4(180 - t) + 35 {measure of t is 35 more than 4 times supplement}
t = 720 - 4t + 35 {used distributive property}
t = -4t + 755 {combined like terms}
5t = 755 {added 4t to both sides}
t = 151 {divided both sides by 5}
180 - t = 29 {substituted 151, in for t, into 180 - t}
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As we know two angles are supplementary if their sum is 180 degree.
Denote x degree the unknown angle, its supplement is 180-x and obtain the equation:
x+35=4(180-x)
-5x=-685
x=137
Answer: The measure of the unknown angle is 137 degree.
