Explain how you can use the triangle sum theorem to find the measures of the angles in an equilateral triangle. the angles of an equilateral triangle are . let the measure of each angle be x. then, by the triangle sum theorem, x + x + x = 3x = ° solving for x gives x = °
The first blank is 180
The second blank is 60
The triangle sum theorem basically says that adding up all three angles of any triangle always leads to 180 degrees. So that's why
(angle1)+(angle2)+(angle3) = 180
x+x+x = 180
3x = 180
Divide both sides of that last equation by 3. This is to undo the multiplication of 3 done to x.
3x = 180
3x/3 = 180/3 ... divide both sides by 3
x = 60
Each angle of this equilateral triangle is 60 degrees. In an equilateral triangle, all three sides are the same length. Also in an equilateral triangle, all three angles are the same measure and always 60 degrees.
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