An angle measures 2 degrees more than 3 times its complement. Find the measure of its complement.?

Question

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Answer 1

Let angle = x
Complement = y
x + y = 90
3y + 2 + y = 90
4y = 88
y = 22 °
x = 68 °

Answer 2

A pair of angles is complementary if the sum of their measures add up to 90 degrees.

If the two complementary angles are adjacent (i.e. have a common vertex and share a side, but do not have any interior points in common) their non-shared sides form a right angle.

In Euclidean geometry, the two acute angles in a right triangle are complementary, because there are 180° in a triangle and 90° have been accounted for by the right angle.

The adjective "complementary" comes from the Latin complementum, which derives from the fourth form of the Latin verb complere, i.e. completum for "having been filled up". An acute angle is filled up by its complement to form a right angle, which is the most basic kind of angle, because it can be constructed by drawing the angle bisector of a line. A right angle is a complete (full) angle.

Source: Wikipedia

The answer to your question would be

Where X is the complementary angle...
X + 3X + 2 = 90
4X + 2 = 90
4X = 90 - 2
X = (90 - 2) / 4
X = 22 degrees

Answer 3

First write out equations for what you know:
a = larger angle
b = smaller angle

90 = a + b
a = 3b + 2
b = 90 - (3b + 2)


Since the equation for b is the only one with 1 variable, you must solve that first:
b = 90 - (3b + 2)
b = 90 - 3b - 2


Combine like terms:
4b = 88


Divide both sides by 4:
b = 22 degrees


Now that you know what b equals, plug its value into the equation for a:
a = 3(22) + 2


Then multiply 3 by 44.5 and add 2:
a = 68


Finally, you have to make sure you did everything correctly, so add the values for a and b to see if they equal 180:
22 + 68 = 90


Everything checks out. Since the question only asks for the size of the complimentary angle (the smaller angle from the way the question was phrased) the answer is 22 degrees.

Answer 4

(1). x + y = 90 & (2). x = 2 + 3y

First: substitute "2+3y" with "x" in the 1st equation.

2+3y + y = 90
2+4y = 90

Sec: combine "like" terms - subtract 2 from both sides (when you move a term to the opposite side, always use the opposite sign).

2-2+4y = 90-2
4y = 88 (Solve for "y" - divide both sides by 4).
4y/4 = 88/4
y = 22

Third: substitue 22 with "y" in the 2nd equation.

(2). x = 2 + 3y
x = 2 + 3(22)
x = 2 + 66
x = 68

SOlutions: 22 & 68 degrees

Answer 5

Complementar angles variety a precise attitude. (ninety levels) So enable's call your attitude a and the 2d attitude 2a+18 or 18 degs greater suitable than two times the orig. attitude. mutually the two angles make ninety levels so upload a to 2a+18 and that they equivalent ninety. a + 2a + 18 = ninety levels. You get 3a=seventy two levels a (orig. attitude) = 24 levels and the 2d attitude is 2x24+18 or66 the respond is d.

Answer 6

Angles that are complement add up to 90 degrees. If angle 'a' is equal to 3b+2, and you want to find b, then
a=3b+2 and a+b=90.

Substituting after rearrangement, this becomes
a=90-b and so 90-b=3b+2

So, finally, you can work out that
88=4b

and so b is equal to 22 degrees!

Answer 7

Let the angle be x.
Its complement is 90 - x
x = 3(90-x) + 2
x = 270 - 3x + 2
4x = 272
x = 68

Answer 8

the angle+the complement together are 90degrees, so you can call the complement x, and "the angle" 3x+2. together they add up to 90 degrees, so 3x+2 + x =90, and solving for x you get 22degrees for the complement

Answer 9

Let x be the complement,

x + (2 + 3x) = 90
4x = 88
x = 22 degrees

Answer 10

let x = complement. then angle is 3x +2

and

3x + 2 + x = 180

4x = 178

x =44.5 deg

angle = 135.5