Final answer:
The described triangle (ΔEFG) is scalene because it has no equal sides or angles, and it is not right-angled as none of the angles are exactly 90°.
Step-by-step explanation:
The given problem describes a triangle (ΔEFG) with the following measurements: E = 31.0 inches, m∠G=89°, and m∠E=27°. A triangle is defined as scalene if it has no sides of equal length, isosceles if at least two sides are of equal length, equilateral if all three sides are equal, and right-angled if one of its angles measures 90°. Given that m∠G is 89°, which is close to 90°, and m∠E is 27°, we can surmise that the triangle is not equilateral or isosceles.
Since the sum of the angles in a triangle equals 180°, we can calculate m∠F as 180° - 89° - 27° = 64°. Since none of the angles are exactly 90°, but one is close, and all angles are different, the triangle is scalene. It is not right-angled because none of the angles are exactly 90°.
To determine the type of triangle, we need to examine the angles and sides. In triangle EFG, we are given that angle G is 89° and angle E is 27°. Since none of the angles are equal, the triangle cannot be equilateral or isosceles. Since the triangle has a 90° angle (angle G), it is a right-angled triangle. Therefore, the correct answer is D. Right-angled.