Converse Parallelogram Proofs Practice

Question

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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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Answer 1

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.

Answer 2

w is not 35 deegrees

Answer 3

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!