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Question

Question
Use the image to answer the question.

A parallelogram upper A upper B upper D upper C has expressions for each angle marked and labeled.

Tiana draws quadrilateral ABCD
as shown, with the measures of∠A, ∠B, ∠C, and ∠D
represented. For what values of m and n is Tiana guaranteed that ABCD
is a parallelogram?
Which is the true opposite angles of m and n
(1 point)
If m=
and n=
, then Tiana is guaranteed that ABCD
is a parallelogram.
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Answer 1

To guarantee that quadrilateral ABCD is a parallelogram, we need to use the properties of angles in a parallelogram:

1. Opposite angles are equal.
2. Consecutive angles are supplementary (add up to 180 degrees).

From the information given, we can ascertain which relationships hold for the angles:

• If \(\angle A = m\),
• \(\angle B = n\),
• \(\angle C\) and \(\angle D\) can be expressed in terms of \(m\) and \(n\) using the properties mentioned above.

For Tiana's quadrilateral ABCD to be a parallelogram, the following conditions must be satisfied:

1. \(m + n = 180^\circ\) (if they are consecutive).
2. \(m = \text{angle C}\) and \(n = \text{angle D}\) (if they are opposite).

Let's summarize the specific angles with respect to their relationships:

• If \(m\) and \(n\) are opposite angles, then:
  • \(m = n\)

You should choose values for \(m\) and \(n\) based on the above conditions.

For example:

• If \(m = 60^\circ\) and \(n = 120^\circ\), then they cannot directly fulfill the properties of a parallelogram. However, if \(m = 70^\circ\) and \(n = 70^\circ\), then ABCD is guaranteed to be a parallelogram because opposite angles are equal.

Please provide the specific angle measures presented in the image to give you exact values. If you require any help understanding the angle relations based on the properties of a parallelogram, let me know!