# Thread: less than 180 degrees = ?

1. ## less than 180 degrees = ?

Random House-A Dictionary of Contemporary American Usage (1957), all:
All the angles in a triangle are less than 180 degrees.

I had thought we should say 'All the angles in a triangle are (= add up to) 180 degrees' and so was very surprised to read the 'less than' in this sentence. To me 'less than 180' means '<180'. But how can the three angles be '<180 degrees'?

2. ## Re: less than 180 degrees = ?

Originally Posted by joham
Random House-A Dictionary of Contemporary American Usage (1957), all:
All the angles in a triangle are less than 180 degrees.

I had thought we should say 'All the angles in a triangle are (= add up to) 180 degrees' and so was very surprised to read the 'less than' in this sentence. To me 'less than 180' means '<180'. But how can the three angles be '<180 degrees'?

"All angles in a triangle are less than 180 degrees" means "Angle A, angle B and angle C are each less than 180 degrees".
"All the angles are ..." does not mean "All the angles add up to ...".
If all the angles in a triangle are 60 degrees, you have an equilateral triangle, having (like all triangles) 180 degrees.

Compare:
All the girls in the family are less than 10 years old. They are 3, 5 and 7.
Their combined age is 15, but they are all under 10.

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