Question
Converse Parallelogram Proofs Practice
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Question
In parallelogram WXYZ, the interior angle of X measures 35 degrees and the interior angle of Z also measures 35 degrees. What are the interior angle measures of W and Y?(1 point)
The interior angle of W
measures
degrees and the interior angle of Y
measures
degrees.
Remaining Attempts : 3
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Answers
GPT-4o mini
In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (add up to 180 degrees).
Given:
- Angle X = 35 degrees
- Angle Z = 35 degrees
Since angle W and angle Z are opposite angles, angle W also measures 35 degrees.
Now, to find angle Y, we can use the fact that angle X and angle Y are supplementary:
Angle X + Angle Y = 180 degrees
35 degrees + Angle Y = 180 degrees
Now, solve for angle Y:
Angle Y = 180 degrees - 35 degrees
Angle Y = 145 degrees
So the measures are:
- The interior angle of W measures 35 degrees.
- The interior angle of Y measures 145 degrees.
Given:
- Angle X = 35 degrees
- Angle Z = 35 degrees
Since angle W and angle Z are opposite angles, angle W also measures 35 degrees.
Now, to find angle Y, we can use the fact that angle X and angle Y are supplementary:
Angle X + Angle Y = 180 degrees
35 degrees + Angle Y = 180 degrees
Now, solve for angle Y:
Angle Y = 180 degrees - 35 degrees
Angle Y = 145 degrees
So the measures are:
- The interior angle of W measures 35 degrees.
- The interior angle of Y measures 145 degrees.
w is not 35 deegrees
GPT-4o mini
I apologize for the oversight in my previous response. Let's go through it step by step correctly this time.
In parallelogram WXYZ, we know:
- Angle X = 35 degrees
- Angle Z = 35 degrees
Since opposite angles in a parallelogram are equal, we confirm:
- Angle W = Angle Y (opposite angle to W is Y)
- Angle W = Angle Z = 35 degrees
Now we need to find the measures of angles W and Y.
Using the property of supplementary angles for consecutive angles:
Angle X + Angle W = 180 degrees
So,
35 degrees + Angle W = 180 degrees
Now, solve for Angle W:
Angle W = 180 degrees - 35 degrees
Angle W = 145 degrees
Since W and Y are opposite angles and angles W and Y are equal, we can conclude:
- The interior angle of W measures 145 degrees.
- The interior angle of Y also measures 145 degrees.
To summarize:
- The interior angle of W measures 145 degrees.
- The interior angle of Y measures 145 degrees.
Thank you for your patience, and I appreciate the correction!
In parallelogram WXYZ, we know:
- Angle X = 35 degrees
- Angle Z = 35 degrees
Since opposite angles in a parallelogram are equal, we confirm:
- Angle W = Angle Y (opposite angle to W is Y)
- Angle W = Angle Z = 35 degrees
Now we need to find the measures of angles W and Y.
Using the property of supplementary angles for consecutive angles:
Angle X + Angle W = 180 degrees
So,
35 degrees + Angle W = 180 degrees
Now, solve for Angle W:
Angle W = 180 degrees - 35 degrees
Angle W = 145 degrees
Since W and Y are opposite angles and angles W and Y are equal, we can conclude:
- The interior angle of W measures 145 degrees.
- The interior angle of Y also measures 145 degrees.
To summarize:
- The interior angle of W measures 145 degrees.
- The interior angle of Y measures 145 degrees.
Thank you for your patience, and I appreciate the correction!