In an equilateral triangle, what is the difference between the sum of the exterior angles and the sum of the interior angles?
In any triangle the two sums would both be 180°.
So the difference between them would be zero.
thankx reiny!
To find the sum of the exterior angles of an equilateral triangle, you can start by knowing that the sum of the exterior angles of any polygon is always 360 degrees.
Now, for an equilateral triangle, each angle measures 60 degrees because all angles in an equilateral triangle are congruent. Therefore, the sum of the exterior angles of an equilateral triangle is 60 + 60 + 60 = 180 degrees.
On the other hand, the sum of the interior angles of any triangle is always 180 degrees. Since an equilateral triangle has three congruent angles, each angle measures 60 degrees. Thus, the sum of the interior angles of an equilateral triangle is 60 + 60 + 60 = 180 degrees.
Therefore, the difference between the sum of the exterior angles and the sum of the interior angles of an equilateral triangle is 180 - 180 = 0 degrees.
To find the difference between the sum of the exterior angles and the sum of the interior angles of an equilateral triangle, let's break it down step by step.
Step 1: Understand the Exterior and Interior Angles
In any polygon, the exterior angles are the angles formed by extending one of the sides of the polygon. On the other hand, the interior angles are the angles formed between the sides of the polygon.
Step 2: Identify the Interior Angles of an Equilateral Triangle
An equilateral triangle is a triangle with all three sides having equal lengths, and all three angles measuring 60 degrees. Since an equilateral triangle has three sides, it also has three interior angles.
Step 3: Calculate the Sum of the Interior Angles
To find the sum of the interior angles of any polygon, you can use the formula: (n - 2) * 180 degrees, where n represents the number of sides. In the case of an equilateral triangle, n is equal to 3. So, the sum of the interior angles of an equilateral triangle is (3 - 2) * 180 degrees, which equals 180 degrees.
Step 4: Calculate the Sum of the Exterior Angles
The sum of the exterior angles of any polygon is always 360 degrees. This means that the sum of the three exterior angles of an equilateral triangle is also 360 degrees.
Step 5: Find the Difference
To find the difference between the sum of the exterior angles and the sum of the interior angles, subtract the sum of the interior angles from the sum of the exterior angles: 360 degrees - 180 degrees. The difference is 180 degrees.
Therefore, in an equilateral triangle, the difference between the sum of the exterior angles and the sum of the interior angles is 180 degrees.