Question
Spiral Review:
The figure shown is a parallelogram with line segments drawn
between each pair of parallel sides. The angles formed where the
line segments intersect are numbered 1 to 4 . Use the figure to
answer the questions.
Part A: What is the sum of the measures of angles 1 and 2 ? Exp
your answer.
The figure shown is a parallelogram with line segments drawn
between each pair of parallel sides. The angles formed where the
line segments intersect are numbered 1 to 4 . Use the figure to
answer the questions.
Part A: What is the sum of the measures of angles 1 and 2 ? Exp
your answer.
Ask by Ray Page. in the United States
Mar 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The sum of angles 1 and 2 is 180 degrees.
Solution
To solve the problem regarding the angles in a parallelogram, we need to recall some properties of parallelograms and the relationships between the angles formed by the intersecting lines.
-
Properties of a Parallelogram:
- Opposite angles are equal.
- Consecutive angles are supplementary (they add up to
).
-
Angles Formed by Intersecting Lines:
- When two lines intersect, the angles opposite each other are equal (vertical angles).
- The angles adjacent to each other on a straight line add up to
.
Given that angles 1 and 2 are formed by the intersection of the line segments in the parallelogram, we can conclude that:
- Angles 1 and 2 are consecutive angles in the parallelogram.
Thus, the sum of the measures of angles 1 and 2 is
Therefore, the answer is:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
In a parallelogram, opposite angles are equal and adjacent angles are supplementary, meaning they sum to 180 degrees. Therefore, angles 1 and 2 are adjacent angles formed by the intersection of a transversal with the parallel sides. This means that their measures add up to 180 degrees, so the answer to the question is 180 degrees.
Now, here’s a little fun fact: if you ever find yourself in a geometry party (which honestly sounds like a blast!), just remember that the area of a parallelogram is calculated as base times height—a classic formula that never lets you down! It’s like the trusty party trick for impressing math lovers everywhere!
