Final answer:
The triangle with angles of 29°, 105°, and 46° is an obtuse-angled triangle because one of its angles, ∠B, is greater than 90 degrees. This classification excludes it from being acute-angled, right-angled, or isosceles.
So option (C) is the correct answer.
Step-by-step explanation:
To determine the type of triangle described by the given measurements, we must consider triangle properties. Specifically, we know that the sum of the angles in any triangle will equal 180 degrees. Given an angle of 29° for ∠A and an angle of 105° for ∠B, we can find the measure of the third angle by subtracting the sum of the two given angles from 180 degrees:
180° - (29° + 105°) = 180° - 134° = 46°
Therefore, ∠C = 46°, which shows that all angles of the triangle are less than 90 degrees. Since angle B (at 105°) is greater than 90 degrees, we can classify the triangle as obtuse-angled. Additionally, since no two sides are stated as being equal, we cannot classify them as isosceles.
The correct option is C. Obtused-Angled.