Question

Tiana draws quadrilateral ABCD as shown, with the measures of ZA, ZB, ∠C, and ∠D represented. For what values of m and n is Tiana guaranteed that ABCD is a parallelogram?
(1 point

Answer 1

To determine the conditions under which quadrilateral ABCD is guaranteed to be a parallelogram, we can use some properties of angles in a parallelogram.

A quadrilateral is a parallelogram if either of the following conditions is satisfied:

1. Opposite angles are equal (for example, \( \angle A = \angle C \) and \( \angle B = \angle D \)).
2. The sum of consecutive angles from one side of the quadrilateral is equal to 180 degrees (for example, \( \angle A + \angle B = 180^\circ \)).

Given that the measures of angles \( \angle A, \angle B, \angle C, \) and \( \angle D \) are in terms of \( m \) and \( n \), you would set up the equations based on either of the above properties.

For instance:
- If \( \angle A = m \), \( \angle B = n \), \( \angle C \), and \( \angle D \) are given in some form (e.g., \( \angle C = x \) and \( \angle D = y \)), you can derive conditions based on the angle relationships.

To specifically answer the question, we need further information about the relationships of angles \( \angle A, \angle B, \angle C, \) and \( \angle D \) in terms of \( m \) and \( n\).

If you can provide the specific values or relationships of these angles, I can help derive the necessary values for \( m \) and \( n\) to ensure that quadrilateral ABCD is a parallelogram.