0
A triangle has 180 degrees because it is a half of a quadrilateral and a quadrilateral can be inscribed within a circle, meaning the quadrilateral has 360 degrees as well, just like the circle. Therefore the triangle has 180. Well, why does a circle have 360 degrees? A lot of our math is based upon astronomy. The degree sign is a circle to represent the sun because it takes the earth 365 days to rotate around the sun. The Babylonians were an intelligent population and they knew this however, they disliked the number 365 for some reason. Therefore, they would count their year with 360 days and just have a party for 5 days straight, pretending that those days don't really count in the year. Therefore, we have 360 degrees in a circle, which leads to the 360 degrees of the quadrilateral, which leads to a triangle, which is half of a quadrilateral meaning it has 180 degrees. This is also where we get 60 minutes in one day, 60 seconds in a minute.
This was proved by Euclid, using the fact that when a transversal cuts across 2 parallel lines, the alternate interior angles are equal (and the parallel postulate). Given a triangle ABC, we use the parallel postulate to draw a line ECF parallel to AB. Then the alternate interior angles CAB and BCF are equal. Likewise, angles CBA and ACE are equal. The angles BCF, ACB, and ACE add up to the straight angle ECF. If equals be added to equals, the sums are equal, so the interior angles of the triangle add up to a straight angle, or 180 degrees.
Add your answer:
Earn +20 pts
Does and isocolies triangle equal 180 degrees?
Assuming the question was if an isosceles triangle have angles that add up to 180 degrees, then yes. All triangles have angles that add up to 180 degrees.
What is the angle of a triangle with 3 equal sides?
A triangle where all three sides are equal is called an equilateral triangle. The sum of all three angles in any triangle is 180 degrees, and since equal sides means equal angles, three equal angles totaling 180 degrees; each angle must be 60 degrees.
What are the angel measurements of an equaliteral triangle?
The angles of an equilateral are the same and since the interior angles of a triangle equal 180 degrees, we know that 180/3=60 degrees.
Are all triangles equal to 180 degrees?
Yes the 3 interior angles of any triangle add up to 180 degrees
All angles in a triangle equal 60 degrees?
If all angles in a triangle are equal to 60 degrees, then the triangle is an equilateral triangle. In an equilateral triangle, all three sides are equal in length. This property is a consequence of the triangle angle sum theorem, which states that the sum of the interior angles of a triangle is always 180 degrees. Therefore, if each angle is 60 degrees, the total sum of the angles in the triangle is 180 degrees, satisfying the theorem.
The sum of a triangle's angles will always equal 180 degrees?
"The sum of the angles in a triangle equal 180 degrees" is a true statement.
What does the perimeter have to equal in a triangle?
180 degrees
What polygon is equal to 180 degrees?
Triangle.
How many degrees is the right triangle?
180 degrees... all triangles equal 180.
How many degrees are in the sum of the angles in a triangle equal?
A triangle equals to 180 degrees
What type of triangle is equal to 180 degrees?
The 3 interior angles of any triangle add up to 180 degrees
What is the difference between an angle and a triangle?
A triangle is made up of 3 angles, which equal 180 degrees.
How many degrees are there in an equalateral triangle?
An equilateral triangle has three equal angles, each measuring 60 degrees. So, there are a total of 180 degrees in an equilateral triangle.
Does the sum of angles of a triangle equal 180 degrees?
Yes, adding up the inner angles of a triangle gives 180 degrees.
What is the sum of angles in a triangle equal to?
180 degrees
What do the 3 sides of a triangle equal in degrees?
180
Is the perimeter of a triangle equal 180?
The sum(addition) of the measures of the three angles of a triangle is 180 degrees.
