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Each angle in an equilateral triangle is...

Each angle in an equilateral triangle is ________

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To solve the question "Each angle in an equilateral triangle is ________", we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Properties of an Equilateral Triangle**: - An equilateral triangle is defined as a triangle where all three sides are of equal length. - Consequently, all three angles in an equilateral triangle are also equal. 2. **Know the Sum of Angles in a Triangle**: - The sum of all interior angles in any triangle is always 180 degrees. 3. **Set Up the Equation**: - Let’s denote each angle of the equilateral triangle as \( A \). - Since all angles are equal, we can express this as: \[ A + A + A = 180^\circ \] - This simplifies to: \[ 3A = 180^\circ \] 4. **Solve for Each Angle**: - To find the measure of angle \( A \), divide both sides of the equation by 3: \[ A = \frac{180^\circ}{3} \] - Performing the division gives: \[ A = 60^\circ \] 5. **Conclusion**: - Therefore, each angle in an equilateral triangle is \( 60^\circ \). ### Final Answer: Each angle in an equilateral triangle is **60 degrees**.
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Which of the following statements are true (T) and which are false (F): Side opposite to equal angles of a triangle may be unequal. Angle opposite to equal sides of a triangle are equal. The measure of each angle of an equilateral triangle is 60^0 If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles. The bisectors of two equal angles of a triangle are equal. If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. The two altitudes corresponding to two equal sides of a triangle need not be equal. If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent. Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.