Complement = 90-x
Supplement=180-x
180-x=4(90-x)+6
180-x=360-4x+6
3x=360-180+6
3x=186
x=186/3
x=62
Complementary angles add up to 90 degrees.
The measure of the angle is 62
Let the angle be x.
So, we have:
[tex]\mathbf{Complement = 90 - x}[/tex]
[tex]\mathbf{Supplement = 180 - x}[/tex]
From the question, we have the following equations
[tex]\mathbf{Supplement = 6 + 4(Complement)}[/tex]
Substitute known values
[tex]\mathbf{180 - x = 6 + 4(90 - x)}[/tex]
Open brackets
[tex]\mathbf{180 - x = 6 + 360 - 4x}[/tex]
Collect like terms
[tex]\mathbf{4x - x = 6 + 360 - 180}[/tex]
[tex]\mathbf{3x = 186}[/tex]
Divide both sides by 3
[tex]\mathbf{x = 62}[/tex]
Hence, the measure of the angle is 62
Read more about complementary and supplementary angles at:
https://brainly.com/question/3027144
