Question
Leopold draws a quadrilateral with two equal angles, Angles 1 and 2. Angle 3 measures 170 degrees, and Angle 4 measures either 55 degrees less than Angle 3 or 55 degrees more than Angle 3. Determine the angle measurement of Angle 2. Show all work.(4 points)
(IN 5 SENTENCES
(IN 5 SENTENCES
Answers
GPT-4o mini
In the given quadrilateral, we know that the sum of the interior angles is 360 degrees. Let Angle 1 and Angle 2 both be \( x \) degrees, Angle 3 be 170 degrees, and Angle 4 be either \( 170 - 55 = 115 \) degrees or \( 170 + 55 = 225 \) degrees.
First, consider when Angle 4 is 115 degrees:
\[ x + x + 170 + 115 = 360 \]
\[ 2x + 285 = 360 \]
\[ 2x = 75 \]
\[ x = 37.5 \]
Next, consider when Angle 4 is 225 degrees:
\[ x + x + 170 + 225 = 360 \]
\[ 2x + 395 = 360 \]
\[ 2x = -35 \] (not valid, as angles cannot be negative)
Thus, the only feasible solution occurs when Angle 4 is 115 degrees, giving us Angle 1 and Angle 2 both equal to \( 37.5 \) degrees. Therefore, Angle 2 measures 37.5 degrees.
First, consider when Angle 4 is 115 degrees:
\[ x + x + 170 + 115 = 360 \]
\[ 2x + 285 = 360 \]
\[ 2x = 75 \]
\[ x = 37.5 \]
Next, consider when Angle 4 is 225 degrees:
\[ x + x + 170 + 225 = 360 \]
\[ 2x + 395 = 360 \]
\[ 2x = -35 \] (not valid, as angles cannot be negative)
Thus, the only feasible solution occurs when Angle 4 is 115 degrees, giving us Angle 1 and Angle 2 both equal to \( 37.5 \) degrees. Therefore, Angle 2 measures 37.5 degrees.