What is the value of e?
Two lines intersect. The upper interior angle measures 122 degrees. The right interior angle is labeled c. The lower interior angle is labeled d. The left interior angle is labeled e.
A. 32°
B. 238°
C. 58°
D. 122°
There is not enough information to determine the value of e.
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To determine the value of angle e, we can use the fact that the sum of interior angles of a quadrilateral is always 360 degrees. In this case, we know the values of two angles, 122 degrees and angle c (unspecified).
Let's assume that angle c is x degrees. Now, let's calculate the sum of the known angles:
122° + x + d + e = 360°
Since the angle measures a quadrilateral, we can say that angle d is also 122 degrees (opposite angles of intersecting lines are equal).
Substituting the values into the equation:
122° + x + 122° + e = 360°
Combine like terms:
2 * 122° + x + e = 360°
2 * 122° = 244° (substituting the value of 122°)
244° + x + e = 360°
Now, isolate the variable e:
e = 360° - 244° - x
So, the value of angle e is 116° - x.
Unfortunately, without knowing the measure of angle c (or x), we cannot determine the exact value of angle e. Therefore, the correct answer to the given options is not provided.