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100 POINTS! Please help, question on the image.

100 POINTS! Please help, question on the image.-example-1
User JBilbo
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2 Answers

5 votes

Answer:

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}}

User Max Xu
by
8.5k points
6 votes

Answer:


\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

User Andy Shulman
by
7.7k points

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