Question: Triangle with Variable Angles

Comment on Triangle with Variable Angles

The sum of exterior angles of a polygon is 360 so 4x+70+155-3x+6x-30 should add up to 360. However this equation does not produce the answer as 15. What can be the possible explanation?
greenlight-admin's picture

Be careful. (6x - 30) is not an exterior angle.

I started plugging in numbers and started with C, which is 15.

4(15) + 70 + x = 180
60 + 70 + x = 180
130 + x = 180
x = 50

130 + 50 = 180 which happened to be 15, the first number I chose.
greenlight-admin's picture

It certainly LOOKS like a valid strategy (since you arrived at the correct answer). However, I'm not 100% I understand what you did.

If you're testing the answer choices and started with answer choice C (15), then you are testing whether or not x = 15. However, as part of your solution, you say that x = 50 (not x = 15), so I'm not sure what's happening there.

Can you tell me a bit more about your solution?


Writing 180-4×+70=250-4x and writing 180-(4x+70)=110-4x yields different answers. What's the importance of these brackets and when do we know how to use it
greenlight-admin's picture

We use brackets around entire entities/values.

For example, one angle measures 4x + 70.
That is, (4x + 70) represents a SINGLE measurement.
So, the angle on the same line will = 180 - (that entire measurement.)
= 180 - (4x + 70)

Does that help?


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