Question
Quadrilateral QRST has vertices at Q (-1, 5), R (2, 8), S (4, 4), and T (1, 1). The measure of Angle Q is 108° and the measure of angle R is 108 - 2x. In 3 sentences in 5th graders response , determine if quadrilateral QRST is a parallelogram, and if so, solve for x. And what is the answer in a math problem (4 points)
Answers
GPT-4o mini
To see if quadrilateral QRST is a parallelogram, we can check the angles. Since the angles in any quadrilateral add up to 360°, we can add the known angles: 108° (Angle Q) + (108 - 2x) (Angle R) + Angle S + Angle T = 360°. If we find Angle S and Angle T are equal when we plug in the value for x, then QRST is a parallelogram!
Now let's solve for x:
1. Set up the equation:
\( 108 + (108 - 2x) + Angle S + Angle T = 360 \)
If we let Angle S and Angle T equal each other, the equation becomes:
\( 216 - 2x + 2*Angle S = 360 \)
which simplifies to \( -2x + 2*Angle S = 144 \)
or \( Angle S = 72 + x \).
2. If we assume Angle S and Angle T are equal, we can plug in to find:
\( 72 + x = 72 + x \) → \( x = 0 \) (which satisfies the condition).
So, QRST **is** a parallelogram because its opposite angles are equal when x = 0!
Now let's solve for x:
1. Set up the equation:
\( 108 + (108 - 2x) + Angle S + Angle T = 360 \)
If we let Angle S and Angle T equal each other, the equation becomes:
\( 216 - 2x + 2*Angle S = 360 \)
which simplifies to \( -2x + 2*Angle S = 144 \)
or \( Angle S = 72 + x \).
2. If we assume Angle S and Angle T are equal, we can plug in to find:
\( 72 + x = 72 + x \) → \( x = 0 \) (which satisfies the condition).
So, QRST **is** a parallelogram because its opposite angles are equal when x = 0!