Question

D E F and A B C are complementary angles and A B C is nine times as large as D E F. Determine the measure of each angle

Answer 1

81, 9

Answer 2

Algebraically this is what you have: Let the measurement of the angle DEF be x and the measurement of the angle ABC be y. For x and y to be complimentary means that when you add them together you get exactly 90 degrees (a right angle). So you have the equation x+y=90 . Now, you also have that y is 9 times as large as x, which boils down to having the equation y=9x . So now you have the equations
x+y=90
y=9x
Two equations and two unknowns perfect so now you can solve for what x and y are.
So you simply substitute y=9x into x+y=90
Step 1) x+y=90
Step 2)Substitute y=9x:
x+(9x)=90
Step 3) Simplify
x+9x=90
10x=90
x=9
Step 4) solve for y,
y=9x
y=9(9)=81
so x=9 and y=81 I'm assuming these are in degrees.

Answer 3

thanks

Answer 4

you're welcome :-)