# Obtaining Angle

#### DaRafster

##### New member
I"m aware all the angles of a triangle can only add up to 180 degrees.

In the attached image, to solve for angle α, I used this formula:

180 - (70 + 60) = 50 degrees

However, I found angle K, not α.

So how would I find the angle? - I know I'm wrong after looking at the answer - which is 130 degrees btw

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#### Dr.Peterson

##### Elite Member
Where did you get your formula? What does it claim to give you?

The fact you mention about the sum of interior angles implies that LKM + 70 + 60 = 180, so that LKM = 180 - (70 + 60) = 50. That justifies your statement that you found "K", assuming you mean LKM.

But angle alpha is the supplement of LKM, which is 180 - 50 = 130 (NOT 30).

There is a theorem, easily proved from the fact you mentioned, that an exterior angle of a triangle is equal to the sum of the other interior angles; so that alpha = 70 + 60 = 130. Can you see how this follows?

#### DaRafster

##### New member
Where did you get your formula? What does it claim to give you?

The fact you mention about the sum of interior angles implies that LKM + 70 + 60 = 180, so that LKM = 180 - (70 + 60) = 50. That justifies your statement that you found "K", assuming you mean LKM.

But angle alpha is the supplement of LKM, which is 180 - 50 = 130 (NOT 30).

There is a theorem, easily proved from the fact you mentioned, that an exterior angle of a triangle is equal to the sum of the other interior angles; so that alpha = 70 + 60 = 130. Can you see how this follows?
Thank you, I can see where this is going. Sorry about the typo btw.
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#### pka

##### Elite Member
Thank you, I can see where this is going. Sorry about the typo btw.
To DaRafster, The external angle theorem states: The measure of any exterior angle of a triangle is equal to the sum of the measures of the opposite interior angles. You should try to prove that. This question is testing your knowledge of that theorem.

#### Jomo

##### Elite Member
what you call angle k and angle a form a straight line, so what is the sum of these two angles? If you know k, then can't you find a?
Do you know a theorem that you can use to get that angle a = 60+70?
Do you know why the sum of the angles in any triangle adds up to 180?