Final answer:
The angle at the peak of an A-Frame house, where the roof meets, is calculated to be 48°. This uses the property that the sum of angles in a triangle is 180°, and therefore the peak angle is found by subtracting the sum of the two 66° ground angles from 180°.
Step-by-step explanation:
The question involves calculating the angle at the peak of an A-Frame house based on the angles at which the roof meets the ground. Given that each side of the roof meets the ground at a 66° angle, we can understand this problem by considering a triangle, where the two ground angles are each 66°, and we need to find the third angle, which is the peak where the two sides of the roof meet.
To calculate this, we utilize the property that the sum of angles in any triangle is 180°. Therefore, the measure of the angle at the peak of the roof is obtained by subtracting the sum of the two ground angles from 180°:
- Sum of angles in a triangle = 180°
- Angle at the peak = 180° - (66° + 66°)
- Angle at the peak = 180° - 132°
- Angle at the peak = 48°