# Exterior angle of a triangle?

1. Dec 4, 2016

### zak100

1. The problem statement, all variables and given/known data

It looks as if 50 degrees is an external angle of the triangle.So it should be greater than the two opposite interior angles (i.e x and the other one). But book tells a different answer. Somebody please guide me.

Zulfi.

2. Relevant equations
No eq. Rule: Exterior angle of a triangle is greater than the two opposite interior angles of atriangle

3. The attempt at a solution
50 degree must be greater than x because it is an exterior angle of a triangle.

Zulfi.

2. Dec 4, 2016

### Buffu

Why do think 50° is an exterior angle ?
Is it contained between two sides of the triangle ?

Last edited: Dec 4, 2016
3. Dec 4, 2016

### Nidum

Does the problem statement tell you what type of triangle it is ?

One particular type of triangle would let you get your answer by inspection . What type would that be ?

Last edited: Dec 4, 2016
4. Dec 4, 2016

### zak100

Hi,
Thanks. Question does not say anything about the triangle. It says that l & k are parallel lines.
I got a explanation of exterior angle from a website:

At each vertex of a triangle, an exterior angle of the triangle may be formed by extending ONE SIDE of the triangle. See picture below.

Its now clear to me whats an exterior angle

I have one another question:
Is the other angle within the triangle, in my question (opposite to x) equals to 50 because its a transversal cutting two parallel lines?
Plz guide me.

Zulfi.

5. Dec 4, 2016

### Nidum

Post removed pro tem .

6. Dec 4, 2016

### zak100

Hi,
<One particular type of triangle would let you get your answer by inspection . What type would that be ?>
Equilateral. In that case x would be 60 which is not same as 50.

Zulfi.

7. Dec 4, 2016

### Buffu

Ok I tell the answer now but first I want to know the reason from you why you think so (state some theorem, law, axiom ... that prompted you to think so).

8. Dec 4, 2016

### Buffu

Then the angle formed by the transversal will also change, So don't think about a special case of the triangle.

9. Dec 4, 2016

### zak100

Hi,

Sorry it not adding the picture. I would ask my question in another post.

Zulfi.

10. Dec 4, 2016

### zak100

Hi,
In the above picture, is y equal to 50?
Zulfi.

11. Dec 4, 2016

### zak100

Hi,
In the following picture, is y equal to 50?

Zulfi.

Last edited by a moderator: Dec 4, 2016
12. Dec 4, 2016

### Buffu

I can't provide you direct answer because the last time I did so, a mentor warned me not to do so.

But I can say if you are right or wrong, if you tell me what do you think about your question with proper reasoning, i.e tell me whether y = 50 or not and justify it.
You might want to use the 'property of angles on the alternate sides of transversal' .

Last edited: Dec 4, 2016
13. Dec 4, 2016

### Staff: Mentor

Your picture is confusing. Is angle y the interior angle that is marked?

14. Dec 6, 2016

### zak100

Hi,
<Is angle y the interior angle that is marked?>
Yes.
<But I can say if you are right or wrong, if you tell me what do you think about your question with proper reasoning, i.e tell me whether y = 50 or not and justify it.>
Actually i already told you about the traversal. Now i am writing the rule:
If a pair of lines is cut by a traversal that is not perpendicular to the parallel lines then:
Four acute angles are equal & four obtuse angles are equal. That's i am thinking that 'y' which i have marked as the interior angle of triangle is equal to 50.
Zulfi.

15. Dec 6, 2016

### Buffu

Yes you are correct. The rule you stated, in short is "Interior angles on the opposite sides of the transversal are equal.".

16. Dec 6, 2016

### Staff: Mentor

In that case, angle y is 50°.