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The two labeled angles are alternate exterior angles, and as such, they are equal. This means that we can set up and solve the following equation:
Answer:
The perimeter of the triangle is approximately equal to 18
Step-by-step explanation:
The coordinates of the vertices of the triangle are (-3, -1), (2, 3), and (5, 2)
The formula for the lengths, l, of the sides of the triangle, given their end points coordinates is presented as follows;
The lengths of the segments that make up the triangle are therefore;
Between the vertex points (-3, -1) and (2, 3), we have, √((-3 - 2)² + (-1 - 3)²) = √41
Between the vertex points (-3, -1) and (5, 2), we have, √((-3 - 5)² + (-1 - 2)²) = √73
Between the vertex points (2, 3) and (5, 2), we have, √((2 - 5)² + (3 - 2)²) = √10
Therefore;
The perimeter of the triangle = The sum of the lengths of the sides of the triangle = √41 + √73 + √10
The perimeter of the triangle = √41 + √73 + √10 ≈ 18.1094
∴ The perimeter of the triangle ≈ 18, after rounding to the nearest whole number.