How would I solve this geometry question?

Question

I asked this before but people did a pretty bad job showing me how they came up with an answer and were clearly in a rush. So please take your time, show me the steps and how you came up with the answer with the answer.

One angle is three less than twice the other. If the angles are complementary, find the number of degrees in each angle.

Answer 1

let A = angle A,  and B = the complement of A

let's suppose that:

A is three less than twice B

then A = 2B - 3

("twice B less three" is the same as "three less than twice B", it is just written backwards)

but since the two angles are complimentary then by definition of complimentary angles:

A + B = 90º

now substitute 2B - 3 for A in the second equation and rewite it:

(2B - 3) + B = 90   and solve it:

3B - 3 = 90

3B = 93

B = 31º and substitute this value for B to find the exact value of A:  A = 2(31) - 3 --> A=62-3 = 59º

Answer 2

Hi,

Let x = "the other angle".

If one angle is three less than twice the other, then it is 2x - 3

If the angles are complementary, then they add to 90

x + 2x - 3 = 90

3x - 3 = 90

3x = 93

x = 31

2x - 3 = 59

The 2 angles are 59 and 31 degrees.

I hope that helps!! :-)

Answer 3

Complementary angles sum to 90 degrees.

Note the use of the following words...

is means "="

twice means *2

three less means -3

let A and B be the measures of the angles

A = 2*B - 3

(A is 3 less than twice the other)

A + B = 90

(They are complementary)

You now have two equations and two unknowns.  Solve the system

A = 2*B - 3

A + B = 90

Substitute the value for A into the second equation....

(2*B - 3) + B = 90

2B - 3 + B = 90

3B - 3 = 90

B - 1 = 30

B = 31

Plug this value back into the second equation....

A + 31 = 90

A = 59

So the angles are 59 and 31 degrees.

Now check

Is 59 three less than twice 31?

Is 59 three less than 62

Is 59 = 59?  CHECK  

Answer 4

if the other angle = x

than the angle that's three less than twice that = 2x-3 because twice the measure of x is 2x and you subtract 3 from that beacuse it's three less than twice the other.

If the angles are complementary that means they add up to 90

so you have x+2x-3=90

3x=93

x=31

the second angle: 90-31=59

so the answer is 31 and 59

Answer 5

If the angles are complementary you know they add up to 90 degrees.

angle 1 + angle 2 = 90

Let x be the second angle.

The first angle then is 2x-3 (twice the other and three less)

Putting it together

(2x-3) + x =90

3x -3 = 90

3x=93

x=31

So the second angle is 31 and the first one is 2(31)-3=59

To check your work :

31 + 59 =90

90=90 check

Answer 6

Complementary angles are two angles that have a measure sum of 90-degrees. Let x be the smaller angle and y be the larger angle. You can make a system of two equations:

y = 2x - 3 (one angle, y, is three less than twice the other, x)

x + y = 90 (the angles are complementary)

Now solve through the substitution method:

x + y = 90 (substitute 2x - 3 for y)

x + 2x - 3 = 90

3x - 3 = 90

3x = 93

x = 31

y = 2x - 3

y = 2(31) - 3

y = 62 - 3

y = 59

ANSWER: The two angles are 31- and 59-degrees.

Answer 7

Its been about 12 years since I took geometry, but here goes.  First, complementary angles, when summed are equal to 90. For example, two angles, one being 30 and the other being 90 would be complementary. Another example would be if one was 89 and the other was 1, these would also be complementary (just an example).  

If one angle is three less than twice the other, let the first angle be called a, while the second angle can be called b, then

a=2b-3

if a + b = 90, then 2b-3+b= 90 and then solve for b.

3b-3=90

3b=93

b= 31

90-b= a

90-31= 59

a= 59, b= 31  

Answer 8

You have two unknown angles, so you need two equations to solve the problem.  We'll call "one angle" x and we'll call the "other" angle y.  So the problem becomes x is 3 less than 2y.  Expressing that as a formula...

x = 2y - 3

This is the first fomula we need to solve the problem.

It is stated that the angles are complementary.  That means that the sum of the two unknown angles, x and y,  is 90 degress.  This provides the second equation we need to solve the problem...

x + y = 90

First, take the first equation and rearrange it so it's in a similar format to the second...

x = 2y -3 is equivalent to -x + 2y = 3

Now it's just a matter of solving the two equations...

x +   y = 90

-x + 2y =   3

-------------------

0 + 3y =  93

       3y = 93

        y = 93/3

        y = 31

To find x, plug in the value of y to either of the two equations...

x + y = 90

x + 31 = 90

x = 90 - 31

x = 59

Confirm the answer by pluging x and y into the other formula...

x = 2y - 3

59 = 2(31) - 3

59 = 62 - 3

59 = 59

The solution is x = 59, y = 31