What is the exterior angle of a triangle?

[zak100]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

50 degree must be greater than x because it is an exterior angle of a triangle.

Somebody please guide me.

Zulfi.

 

[Buffu]

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

 

[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 ?

 

[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 what's 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.

 

[Nidum]

Post removed pro tem .

 

[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.

 

[Buffu]

Is the other angle within the triangle, in my question (opposite to x) equals to 50 because its a transversal cutting two parallel lines?

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).

 

[Buffu]

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.

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

 

[zak100]

Hi,
Thanks for your reply.Sorry it not adding the picture. I would ask my question in another post.Zulfi.

 

[zak100]

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

 

[zak100]

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

Zulfi.

 

[Buffu]

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

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' .

 

[Mark44]

Hi,
In the following picture, is y equal to 50?
View attachment 109903
Zulfi.

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

 

[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.

 

[Buffu]

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.

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

 

[Mark44]

Hi,
<Is angle y the interior angle that is marked?>
Yes.

In that case, angle y is 50°.