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Question

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anonymous · Answer

Firstly, it's important to notice that $\bf m\angle 2=m\angle 1=x+50$.
Also notice this: $\bf m\angle 2 + m\angle 5=m\angle 1 + m\angle5=(x+50)+(4x-30)=180$.

After simplifying we get: $\bf 5x+20=180 \implies x = 32$

Now plug this value in back for 'x' in the original equation we are given for $\bf m\angle 2=m\angle 1$.

And that's it.

@MayMay_69

anonymous · Answer

No no. Remember what I said, Angle 1 and Angle 2 are equal, do you agree with me?

anonymous · Answer

@MayMay_69 Please reply.

anonymous · Answer

|dw:1374836375328:dw| MayMay try this if you see in the drawing angles in opposite directions are same

anonymous · Answer

Ok I'll show you why angle 1 and angle 2 are equal:|dw:1374836481580:dw|When you have two lines intersecting like that, the angle they make with each other is the same on both sides. In the diagram of the question we have:|dw:1374836566467:dw| We see the same thing here and so angle 1 and 2 are equal.

anonymous · Answer

Since we are given that $\bf m\angle 2=x+50$, and we concluded from above that angle 2 and angle 1 are equal, then angle one must also be $\bf x + 50$. Are you with me so far?

@MayMay_69

anonymous · Answer

Ok, good. Now the next crucial observation we must make is that angle 2 + angle 5 = 180, i.e. $\bf m \angle 2 + m\angle 5 =180$.

Do you know where I'm getting this from? 

@MayMay_69

anonymous · Answer

@MayMay_69 You know the cycle, you have to reply...

anonymous · Answer

hope this helps @MayMay_69

anonymous · Answer

@BarbaraKara that's a very nice solution which is what I also concluded but @MayMay_69 isn't replying..

anonymous · Answer

@MayMay_69 barbara posted a nice solution that is hand-written. Take a look at it. If you are still confused, ask and I'll respond.

anonymous · Answer

Can you see the attachement @MayMay_69 ? it might take a while to load if your internet is slow.. patience..haha

anonymous · Answer

To solve for x, you need to know a VERY IMPORTANT rule !!

This rule is that when you have PARALLEL LINES and

When you have a line going straight through the PARALLEL LINES,

the two angles sitting in between (CO-INTERIOR ANGLES) (AS YOU CAN SEE IN MY DIAGRAM) 

******WILL ALWAYS ADD UP TO 180 DEGREES*********

So, what are these two angles which are given to you?

anonymous · Answer

It's 82.... @MayMay_69

anonymous · Answer

Although you should really try understand how we got to the answer rather than asking us to tell you what the answer is.