Which Set Of Angles Can Form A Triangle?

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What is a Triangle?

A triangle is a polygon with three straight sides and three angles. It is one of the basic shapes in geometry. The three angles of a triangle always add up to 180°. The sum of the internal angles of any polygon, no matter how many sides it has, is always equal to 180° multiplied by the number of triangles minus two.

Types of Triangles

Triangles are classified based on the lengths of their sides and the measure of their angles. The three types of triangles are equilateral, isosceles, and scalene triangles. An equilateral triangle has three equal sides and three equal angles that measure 60° each. An isosceles triangle has two equal sides and two equal angles. A scalene triangle has three different sides and three different angles.

What Sets of Angles Can Form a Triangle?

To form a triangle, the sum of any two angles must always be greater than the measure of the third angle. The two angles must add up to more than 180°. For example, if one angle measures 40°, then the other two angles must add up to more than 140°. This means that the two angles can measure 80° and 60°, or they can measure any other combination of angles that add up to more than 140°.

Angles of a Triangle

The angles of a triangle are always less than 180°. The sum of the three angles of a triangle is always 180°. This is because any triangle can be divided into two right triangles, and the sum of the three angles of any right triangle is always 180°. This means that the three angles of any triangle must add up to 180°.

Angles of an Isosceles Triangle

The angles of an isosceles triangle are always equal. This means that the two equal angles must be greater than the measure of the third angle. For example, if one angle measures 40°, then the other two angles must each measure at least 70°. This means that the two equal angles must add up to at least 140°.

Angles of an Equilateral Triangle

The angles of an equilateral triangle are always equal. This means that each angle must measure 60°. This means that the sum of the three angles of an equilateral triangle is always equal to 180°.

Angles of a Scalene Triangle

The angles of a scalene triangle are always different. This means that the three angles can measure any combination of angles that add up to 180°. For example, one angle can measure 40°, and the other two angles can measure 70° and 70°. This means that the three angles of a scalene triangle must add up to 180°.

Conclusion

To form a triangle, the sum of any two angles must always be greater than the measure of the third angle. The three angles of a triangle must always add up to 180°. The angles of an isosceles triangle must be greater than the measure of the third angle. The angles of an equilateral triangle must each measure 60°. The three angles of a scalene triangle can measure any combination of angles that add up to 180°.

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