im doing angles and such...how can you find the measurements of all angles when you only know one measurement? for example:
angle BOA=100 degrees
now how would i find the other angle's measurements? i know about supplementary but is there a trick to use or a key??
That all depends upon what kind of "other angles" you are talking about. Complementary? supplemetary? internal? external? Right triangle angles?
internal external supplementary all that stuff
To find the measurements of other angles when you know one measurement, there are a few key concepts and relationships that you can use.
1. Supplementary angles: Supplementary angles are two angles whose sum is 180 degrees. If you know the measurement of one angle, you can subtract it from 180 to find the measurement of the other angle. For example, if angle BOA measures 100 degrees, then angle AOB would be 180 - 100 = 80 degrees.
2. Complementary angles: Complementary angles are two angles whose sum is 90 degrees. If you know the measurement of one angle, you can subtract it from 90 to find the measurement of the other angle. However, in your example, angle BOA does not provide enough information to find its complementary angle.
3. Vertical angles: Vertical angles are the pairs of opposite angles formed by two intersecting lines. Vertical angles are always congruent (equal). So, if you know the measurement of one vertical angle, you can directly apply that measurement to the other vertical angle. In your case, if angle BOA measures 100 degrees, then the vertical angle opposite to it (angle AOB) would also measure 100 degrees.
4. Parallel lines and transversals: If you have parallel lines intersected by a transversal, certain angle relationships can be used to find the measurements of other angles. Some of the key relationships are:
- Corresponding angles: Corresponding angles are pair of angles formed on the same side of the transversal and at the same position relative to the parallel lines. Corresponding angles are congruent. If you know the measurement of one corresponding angle, you can directly apply that measurement to the other corresponding angle.
- Alternate interior angles: Alternate interior angles are pair of angles formed on different sides of the transversal and inside the parallel lines. Alternate interior angles are congruent. If you know the measurement of one alternate interior angle, you can directly apply that measurement to the other alternate interior angle.
- Alternate exterior angles: Alternate exterior angles are pair of angles formed on different sides of the transversal and outside the parallel lines. Alternate exterior angles are congruent. If you know the measurement of one alternate exterior angle, you can directly apply that measurement to the other alternate exterior angle.
These angle relationships provide a systematic way to find the measurements of other angles when you only know the measurement of one angle. By using these relationships, you can navigate through the given angles and apply the appropriate relationship to find the missing measurements.