Answer:140 degrees
Explanation:
The sum of the exterior angles of any polygon is always 360 degrees. In a triangle, the sum of the three exterior angles is equal to 360 degrees. Let's denote the measures of the exterior angles as 4x, 7x, and 7x, where x is a constant. Since the sum of the exterior angles of a triangle is 360 degrees, we can write the equation: 4x + 7x + 7x = 360 Combining like terms, we get: 18x = 360 To solve for x, we divide both sides of the equation by 18: x = 360 / 18 Simplifying, we find: x = 20 Now that we know the value of x, we can substitute it back into the expressions for the exterior angles: 4x = 4 * 20 = 80 degrees 7x = 7 * 20 = 140 degrees 7x = 7 * 20 = 140 degrees The largest interior angle of a triangle is opposite the longest side. In this case, the longest side corresponds to the largest exterior angle, which measures 140 degrees. Therefore, the measure of the largest interior angle of the triangle is 140 degrees.