Final answer:
The two interior acute angles formed by the shelving bracket that makes an exterior angle of 132° with the wall are 48° and 90°. The 90° angle is due to the shelf being perpendicular to the wall, and the 48° angle is found by subtracting the exterior angle from 180°.
Step-by-step explanation:
The question revolves around a shelf that is perpendicular to the wall, with a shelving bracket creating an exterior angle with the wall. When a shelf is perfectly perpendicular to a wall, the interior angle between the shelf and the wall would be 90°. However, the exterior angle given is 132°, which is supplementary to the interior angle, i.e., they sum up to 180°.
To find the two interior acute angles shown, we need to subtract the exterior angle from 180° to get the interior angle attached to it. This would be 180° - 132° = 48°. Since the shelf is perpendicular to the wall, one of the interior acute angles would be 90° by definition. Therefore, the measures of the two interior acute angles would be 48° (for the angle adjacent to the exterior angle) and 90° (between the shelf and the wall), which corresponds to option D and option E, respectively.