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We are given the three following triangles.
The smallest triangle is equilateral. The two larger triangles are made of copies of the smallest triangle. We want to find the measure of each interior angle in each of the three given triangles. Let's start with the smallest triangle. Recall the rule for the sum of the measures of the interior angles of a polygon.
Interior Angle Sum of a Polygon |
The sum of the measures of the interior angles of a polygon is (n−2)180, where n represents the number of sides. |
Since the two larger triangles are made of copies of the smallest triangle, we can write all the missing angle measures in these triangles.
Finally, we got that the measure of each interior angle in each of the three given triangles is 60∘. Moreover, we can see that the two larger triangles are also equilateral. If the side length of the smallest triangle is a, the side length of the two larger triangles are 2a and 3a.
Therefore, we can make a conjecture that no matter how large an equilateral triangle is, each interior angle measure of the triangle is 60∘.