PLEASE HELP ME with my geometry homework?

Question

i really need help because i dont understand it and neither do my brother nor my mom.

1. the supplement of an angle is 8 degrees less than 3 times the measure of the angle. find the angle measure.

2. 2 angles are complementary. 4 times the measure of the smaller is half the measure of the larger. find both angle measures.

3. 2 angles are complementary. the measure of one angle is one-fourth of the other. what are the angle measures?

4. the complement of an angle is 8 degrees less than 1/3 of the angles supplement. find the angle measure

PLEASE PLEASE HELP ME. these are the only problems i dont get

Answer 1

Hi,

1. the supplement of an angle is 8 degrees less than 3 times the measure of the angle. find the angle measure.

Let x = angle
Then 3x - 8 = its supplement
Since supplementary angles add to 180:
x + 3x - 8 = 180
4x - 8 = 180
4x = 188
x = 47°
3x - 8 = 133°

2. 2 angles are complementary. 4 times the measure of the smaller is half the measure of the larger. find both angle measures.
Complementary angles add up to 90°. If x is the smaller angle, then 90 - x is the larger angle. 4 times the smaller is 4x and half the larger is ½(90 - x). The equation is:

4x = ½(90 - x)
8x = 90 - x
9x = 90
x = 10°
90 - x = 80°


3. 2 angles are complementary. the measure of one angle is one-fourth of the other. what are the angle measures?
Complementary angles add to 90.
If x is one angle then ¼x is the other angle.

x + ¼x = 90
5/4x = 90
4/5(5/4x) = 4/5(90)
x = 72°
90 - x = 18°


4. the complement of an angle is 8 degrees less than 1/3 of the angles supplement. find the angle measure
If x = angle, then its complement is 90 - x and its supplement is 180 - x.

If complement is 8° less than 1/3 of the supplement, then:

90 - x = 1/3(180 - x) - 8
98 - x = 1/3(180 - x)
3(98 - x) = 180 - x
294 - 3x = 180 - x
294 = 180 + 2x
114 = 2x
57 = x
Its complement is 33° and its supplement is 123°
33 is 8 less than 1/3 of 123 because 33 = 41 - 8

I hope those help!! :-)

Answer 2

Supplementary angles add up to 180 degrees.
Complementary angles add up to 90 degrees.

1. Let A be the angle.
The supplement of A is 3A - 8.
So: A + (3A - 8) = 180 and 4A = 188
A = 188/4 = 47

2. Let A and B be the two angles
They are complementary so A + B = 90
Now call A the larger angle so 4B = A/2
Solve this last equation for A and get A = 8B
8B + B = 90 and 9B = 90
B = 10 and A = 80

3. Let A and B be the two angles
They are complementary so A + B = 90
Measure of one angle is 1/4 the other so A = B/4
Then: B/4 + B = 90
B + 4B = 360 = 5B and B = 360/5
B = 72 and A = 18

4. Let A and B be the two angles
They are complementary so A + B = 90

Now B is 8 degrees less than 1/3 the supplement so
Supplement = 180 - A so B = (1/3)(180 - A) - 8
A + (1/3)(180 - A) - 8 = 90
A + 60 - A/3 = 98
(2/3)A = 38 and A = 38(3/2)
A = 57

Check: 90 - 57 = 33 (the complement)
180 - 57 = 123 (the supplement)
(1/3)123 - 8 = 41 - 8 = 33 and the answer is good

I only checked the last one but all the questions can and should be checked. This should always be done when working out math problems.

Answer 3

yea as the first answer said
1) x + (3x - 8) = 180

here a formulas to help you out with each problem

2) 2 angles x and y
x + y = 90 and 4x = (1/2)y

3) 2 angles x and y
x + y = 90 and x = (1/4)y

4) 3 angles x, y, and z (you want to solve for x)
x + y = 90 , x + z = 180 and y = (1/3)z - 8

Answer 4

Two angles are supplements of each other if they add up to 180 degrees

Two angles are compliments of each other if they add up to 90 degrees

You need to come up with equations using these facts.
Example for #1) (x) + (3x-8) = 180 solve for x

Answer 5

1. Let x = the angle
Then 180-x = its supplement
So 180 - x = 3x-8
188 = 4x
x = 47 degrees

2. Let x = smaller angle
Then 90-x = larger angle
So 4x = (90-x)/2
8x =90 -x
9x= 90
x=10 degrees
90-x = 80 degrees

3. x = one angle
90-x = other angle
x/4 = 90-x
x = 360 -4x
5x =360
x =72 degrees
90-x = 18 degrees

4. x= the angle
The 90-x = its complement, and
180 - x = its supplemt
So, 90-x = 1/3(180-x)-8
98 -x = 1/3(180-x)
294-3x = 180 -x
294-180 = 3x - x
114 = 2x
x = 57