1 math question that I've been stuck on for days!!?

Question

someone please help me I've been trying to figure this out for days now.. I'm trying to help my son with his math homework and I want to make sure I have the right answer but I ca't figure it out



Solve for the value of y and the measures of angles 1 and 3. Please show work. One of the lines crosses another line to form four angles labeled clockwise 1,2,3, and 4. The measures of these angles are:
(angle 1)M<1 = (6y +29)
(angle 2)M<2 = (4x+31)
(angle 3)M<3 = (1 2y -7)
(angle 4)M<4 = (6x - 11 )

Answer 1

Angles (1) and (3) are vertical angles (the pair of angles that are directly across from each other when two straight lines intersect), therefore equal. Equate angles (1) and (3):

6y + 29 = 12y - 7 -->
6y -12y = -7 - 29 -->
-6y = -36 -->
y = 6

Likewise, angles (2) and (4) are equal. Therefore equate:

4x + 31 = 6x - 11 -->
4x - 6x = -11 -31 -->
-2x = -42 -->
x = 21

Verification: Plug x=21, y=6 in the measures and calculate each angle. Then add; they should add up to 360 degrees:

M1 = 6*6 + 29 = 36 + 29 = 65
M2 = 4*21 + 31 = 84 + 31 = 115
M3 = 12*6 - 7 = 72 - 7 = 65 (equals angle M1)
M4 = 6*21 - 11 = 126 - 11 = 115 (equals angle M2)

Add: 65+115+65+115 = 360

Answer 2

When two lines intersect to form 4 angles and if the angles are measured 1, 2, 3, 4 clockwise, then

m<1 = m<3

m<2 = m<4

because they are pairs of opposite angles.

so
6y + 29 = 12y - 7

subtract 6y

29 = 6y - 7

add 7

36 = 6y

y = 36/6 = 6

m<1 = m<3 = 6(6) + 29 = 36+29 = 65 degrees

similarly

4x + 31 = 6x - 11

2x = 42

x = 21

m<2 = m<4 = 4x+31 = 4(21) +31 = 84 + 31 = 115 degrees

note: sum of all the angles(1,2,3,4) should add up to 360

because they form full circle. here 2(65 + 115) = 2(180) = 360

and (1+2) = (3+ 4) = 180 because they form linear pair

Answer 3

Unfortunately, your question is not entirely clear, especially without the accompanying diagram, but from what I understand, two lines cut each other and make four angles, correct? Now, since the opposite angles would be equal in this case, the measures of angles 1 and 3 (and 2 and 4) would be the same. So, putting this information in an equation gives us:

6y+29 = 12y-7
6y = 36
y = 6

Which gives the measure of angle 1 (and that of 3) to be 65 degrees (by substituting the value for y).

If you want to also find the value of x and the measures of angles 2 and 4, remember that adding up angles 1 and 2 (and 3 and 4) would give us 180 degrees, and since angle 1 is 65 degrees, this makes the measure of angle 2 to be 115 degrees, and then use this information to solve for x.

Answer 4

Vertical angles are equal so angle 1 = angle 3 and angle 2 = angle 4.
So 6y+29 = 12y-7
6y =36
y = 6
So angle 1 = angle 3 = 65 degrees
4x+31=6x-11
2x = 42
x =21
So angle 2=angle 4 = 115 degrees
This checks because angle 1 + angle 2 = 115+65 = 180 = a straight line.

Answer 5

Angles (1, 2) (2,3) (3,4) and (4,1) are supplementary, meaning they form a line together. And because of that, they add up to 180 degrees (measure of a line).

(6y+29) + (4x+31) = 180
(12y-7) + (6x-11) = 180

You now have 2 equations and 2 unknowns to solve for.

Edit: You're thinking of Vertical Angles, Endo.

Answer 6

To solve this problem you must first recognize that angles 1 & 3 and 2 & 4 are equal. (For the life of me I cannot remember the name of this identity!) Once you recognize that you can set the x functions and the y functions equal to each other.

4x + 31 = 6x-11
6y + 29 = 12y - 7 (That is supposed to be 12y, right?)

No just solve for x and y:
x = 21
y = 6

Answer 7

when two lines cross each other, the vertically opposite angles are equal. so
M of angle1=M of angle 3
6y+29=12y-7
6y=36
y=6. ANS.
M of angle 1 =6*6+29=65degrees
=65degrees. ANS.
Excellent father!
measureof angle 3 is also 7degrees

Answer 8

opposing angles will be equal. so <1 and <3 are equal
and <2 and <4 are equal.

set equations to each other and solve.

Answer 9

The answer is 42.