Question

100 POINTS! Please help, question on the image.

Answer 1

x = 9, y = 6

Explanation:

According to the Consecutive Interior Angles Theorem, the pair of consecutive interior angles formed when two parallel lines are cut by a transversal are supplementary (sum to 180°).

Therefore, we can create two equations from the given diagram:

`(3x+y)^(\circ)+147^(\circ)=180^(\circ)\implies 3x+y+147=180`

`(3x-y)^(\circ)+159^(\circ)=180^(\circ)\implies 3x-y+159=180`

Add the two equations to eliminate the terms in y:

`\begin{array}{crcccccl}&3x&+&y&+&147&=&180\\\vphantom{\frac12}+&(3x&-&y&+&159&=&180)\\\cline{2-8}\vphantom{\frac12}&6x&&&+&306&=&360\end{array}`

Solve the equation for x:

`\begin{aligned}6x+306&=360\\6x+306-306&=360-306\\6x&=54\\6x/ 6&=54 / 6\\x&=9\end{aligned}`

Substitute the found value of x into one of the equations, and solve for y:

`\begin{aligned}3x+y+147&=180\\\\\implies 3(9)+y+147&=180\\27+y+147&=180\\y+174&=180\\y+174-174&=180-174\\y&=6\end{aligned}`

Therefore, the solution is:

`\Large\boxed{\boxed{x=9,\;\;y=6}}`

Answer 2

`\sf x =9, y = 6`

Explanation:

Before answering this question, we need to know about the co interior angle.

Co-interior angles are two interior angles of two parallel lines that lie on the same side of a transversal.

Properties of co-interior angles:

• Co-interior angles are supplementary, meaning that they add up to 180°.
• If two angles are supplementary, then the lines containing the angles must be parallel.

In this case:

We need to use it twice.

Since Co-interior angles are supplementary, meaning that they add up to 180°.

Using this:

For Upper Co-interior angle

`\sf 147^\circ + (3x + y )^\circ = 180^\circ`

For lower co-interior angle

`\sf 159^\circ + (3x - y )^\circ = 180^\circ`

Now

Adding both equation, we get

`\sf 147^\circ + (3x + y ) ^\circ+ 159^\circ + (3x - y ) ^\circ = 180^\circ + 180^\circ`

Simplify like terms:

`\sf 306^\circ + 6x = 360^\circ`

Subtract 306° on both side, we get

`\sf 6x = 360^\circ - 306^\circ`

`\sf 6x = 54^circ`

Divide both sides by 6.

`\sf x = (54)/(6)`

`\sf x = 9`

Substitute the value of x in any equation, we get

`\sf 159^\circ + (3* 9 - y )^\circ = 180^\circ`

`\sf 159^\circ + (27 - y )^\circ = 180^\circ`

`\sf 159^\circ + 27^\circ (- y )^\circ = 180^\circ`

Simplify like terms:

`\sf 186^\circ -y^\circ= 180^\circ`

Add y and subtract 180° on both sides, we get

`\sf y = 186 - 180`

`\sf y = 6`

So,

answer is:

`\sf x =9, y = 6`