Question

Two lines are intersected by a third line. If angle2 = 226 deg, which must be true about angle2?

1. ∠2 is acute.
2. ∠2 is obtuse.
3. ∠2 measures 5/6 of a full circle.
4. ∠2 measures 7/8 of a full circle.

Answer 1

Angle2, which measures 226 degrees, is greater than 180 degrees and therefore is an obtuse angle. It is neither acute nor equal to 5/6 or 7/8 of a full circle.

Step-by-step explanation:

If angle2 = 226 degrees, we need to determine its characteristics. According to angle measurements, any angle greater than 90 degrees and less than 180 degrees is considered an obtuse angle. Given that angle2 is 226 degrees, it is greater than both 90 degrees and 180 degrees, which means it cannot be acute. Acute angles are less than 90 degrees. Since a full circle is 360 degrees, if we calculate the fraction of the full circle that angle2 represents, we get 226/360 which simplifies to 113/180. This fraction does not equal either 5/6 (which is 300/360) or 7/8 (which is 315/360). Therefore, the correct statement about angle2 is that it is an obtuse angle.