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Chapter 1: Problem 26

What can you say about the measures of the angles in an equilateral triangle?

Short Answer

Expert verified
In an equilateral triangle, all three angles are equal in measure. The sum of angles in any triangle is 180 degrees. Therefore, in an equilateral triangle, each angle measures \(\frac{180}{3} = 60\) degrees.

Step by step solution

01

Equilateral Triangle Definition

An equilateral triangle is a triangle with all three sides of equal length, and all three angles are also equal in measure.
02

Sum of Angles in a Triangle

In every triangle, the sum of all three angles is always 180 degrees.
03

Finding the Measure of Each Angle

Since we know that all three angles in an equilateral triangle are equal and the sum of angles in any triangle is 180 degrees, we can find the measure of each angle by dividing 180 by the number of angles (3). \[ \text{Measure of each angle} = \frac{180}{3} \]
04

Calculating the Measure of Each Angle

Calculate the measure of each angle by dividing 180 by 3: \[ \frac{180}{3} = 60 \]
05

Conclusion

In an equilateral triangle, all three angles measure 60 degrees.

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