A carpenter is making a brace for a chair. To do so she intersect two pieces of wood to make two sets of vertical angles. The obtuse angles formed are 145°. what is the measurement for each acute angle formed
The Correct Answer and Explanation is:
ChatGPT said:
Correct Answer: 35°
Explanation:
When two straight lines intersect, they form two pairs of vertical angles (also known as opposite angles). Vertical angles are always equal to each other. At the same time, each pair of adjacent angles formed by the intersection are supplementary, meaning they add up to 180°.
In this case, the carpenter intersects two pieces of wood to form two sets of vertical angles. Among these, the obtuse angles are each measured at 145°. Since vertical angles are equal, that means there are two angles of 145°, directly opposite each other.
Now, let’s determine the measure of the acute angles formed.
Each acute angle is adjacent to an obtuse angle of 145°. Because adjacent angles along a straight line must add up to 180°, we subtract the obtuse angle from 180°:180∘−145∘=35∘180^\circ – 145^\circ = 35^\circ180∘−145∘=35∘
So, each acute angle measures 35°. Since there are two obtuse angles (145° each), and their adjacent angles must also be equal due to the vertical angle rule, there must also be two acute angles, each measuring 35°.
To summarize:
- Vertical angles are equal.
- Adjacent angles are supplementary (they add up to 180°).
- If one angle is 145°, its adjacent angle must be 180∘−145∘=35∘180^\circ – 145^\circ = 35^\circ180∘−145∘=35∘.
- Therefore, the acute angles formed by the intersecting wood pieces are 35° each.
This understanding is essential not only in carpentry but also in geometry, design, and construction, where precise angle measurements affect the strength and symmetry of structures. Making sure that the correct angles are used ensures that the chair brace is both strong and visually balanced.
