Recall that two angles are complementary if the sum of their measures is 90degrees. Find the measures of two complementary angles if one angle is 6 degrees more than two times the other angle?

word problems

2 Answers
Oct 10, 2017

28 and 62 degrees

Explanation:

Let A=the measure of the smaller angle
B=the measure of the larger angle

Since they are complementary A+B=90

We also know 2A+6=B

Replace B in the first equation with the second equation:

A+2A+6=90

Solve for A:

3A+6=90
3A=84
A=28

So: B=2(28)+6=62

So the two angles are: 28 and 62 degrees

Oct 10, 2017

One is 28^o and the other is 62^o

Explanation:

Condition 1: Their sum is 90^o

Dropping the degrees sign for now.

Condition 2:

Let the first angle be x
Let the second angle be y

Then form the question

"if one angle "...................->x
"is" ..................................->x=?
"6^o more than ".................->x=?+6
" 2 times the other angle "..->x=2?+6" "->" "x=2y+6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This gives us two equations

x+y=90" ".......................Equation(1)
x=2y+6" ".......................Equation(2)

Method: change these so that we have 1 equation with 1 unknown and thus solvable.

color(blue)("Determine the value of "y)

Using Equation(1) to remove one of the unknowns in Equation(2)

Consider Equation(1)

Subtract color(red)(y) from both sides

color(green)(x+y=90 color(white)("ddd")->color(white)("ddd") x+ycolor(red)(-y)=90color(red)(-y))

color(white)("dddddddddddd")->color(white)("dddd")x=90-y" ".....Equation(1_a)

color(brown)("Notice that this has the same consequence as the shortcut")color(brown)("approach of move to the other side and reverse the sign from + to -")
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using Equation(1_a) substitute for x in Equation(2)

color(green)(color(red)(x)=2y+6color(white)("ddd")->color(white)("ddd")color(red)(90-y)=2y+6)

Using the shortcut approach we have:

84=3y

The 3's sign is multiply so the shortcut is move to the other side and reverse the sign from xx" to "-: giving:

84/3=y

Write as y=84/3 as this complies with convention

color(white)("ddddddddddd")ul(bar(|color(white)("d")y=84/3 = 28color(white)("d")|))
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Determine the value of "x)

Using Equation(1)

x+y=90

x=90-28

color(white)("ddddddddddd")ul(bar(|color(white)(2/2)x=62color(white)(2/2)|))
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Check")

2(color(red)(28))+6->56+6=62