1. The integers are: 2,4 and 6
2. The angle is 45°
Step-by-step explanation:
1. Find three consecutive even integers, such that 8 times of the first integer 6 more than the sum of second and third integers.
Let x be the first even integer then net two integers will be x+2 and x+4
According to the given statement
[tex]8x=x+2+x+4+6\\8x=2x+12[/tex]
Subtracting 2x from both sides
[tex]8x-2x=2x+12-2x\\6x=12[/tex]
Dividing both sides by 6
[tex]\frac{6x}{6}=\frac{12}{6}\\x=2[/tex]
The other integers will be:
x+2 = 2+2 = 4
x+4 = 2+4 = 6
Hence,
The integers are: 2,4 and 6
2. Find the measure of an angle whose supplement id three times its complement.
Let x be the required angle
then its supplement will be 180-x
and complement will be 90-x
Then according to given statement
[tex]180-x=3(90-x)\\180-x=270-3x[/tex]
Adding 3x on both sides
[tex]180-x+3x=270-3x+3x\\180+2x=270[/tex]
Subtracting 180 from both sides
[tex]180+2x-180=270-180\\2x=90[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{90}{2}\\x=45[/tex]
Hence,
The angle is 45°
Keywords: Angles, Integers
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