Answer:
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Step-by-step explan
To prove that the sum of the measures of the interior angles of a triangle is 180°, let's start by creating a triangle and examining its angles.
Step 1: Create a Triangle
We will create a triangle and label its angles as A, B, and C.
A
/\
/ \
/____\
B C
Step 2: Measure the Angles
Using a protractor or by assuming arbitrary values for the angles, measure the angles A, B, and C. Let's assume that angle A measures x°, angle B measures y°, and angle C measures z°.
Step 3: Analyze the Triangle
Now, let's analyze the triangle and its angles.
The sum of the measures of the interior angles of any triangle is always 180°.
Each angle of a triangle is adjacent to two other angles.
Step 4: Apply the Angle Sum Property
According to the angle sum property of a triangle, the sum of the measures of the interior angles of a triangle is always 180°.
Therefore, the sum of angle A, angle B, and angle C is:
x° + y° + z° = 180°
Thus, we have proved that the sum of the measures of the interior angles of a triangle is 180°.
Note: This proof holds true for all triangles, regardless of their size or shape.