Answer:
Step-by-step explanation:
angle:: x
complemet: 90-x
supplement: 180-x
Equation:
180-x = 4(90-x)+60
180-x = 360 -4x + 60
3x = 240
x = 80 degrees (the angle)
90-x = 10 degrees (the complement)
180-x = 100 degrees (the supplement)
If the measure of the supplement of an angle is 60 degrees less than four times the measure of the complement of the angle, the required angle will be 40degrees.
Let the measure of the required angle be x
Supplement of the angle = 180 - x ....................1
Complement of the angle = 90 - x
four times the measure of the complement of the angle = 4(90-x)
60 degrees less than four times the measure of the complement of the angle = 4(90-x) - 60 ................................ 2
Equate 1 and 2 to get the unknown value 'x'
180 - x = 4(90-x) - 60
180 - x = 360-4x-60
180 - x = 300 - 4x
Collect the like terms
-x + 4x = 300 - 180
3x = 120
Divide both sides by 3
3x/3 = 120/3
x = 40
Hence the measure of the required angle is 40 degrees
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