Linear Angles ExamplesExamples of linear angles
Linear angle pair
The two neighboring angles should make a linear angle couple if their unusual branches are two opposite beams. ?AOC and BOCTOR. AOC and BOCTOR. AOC and BOC form a linear angle couple. Phrase 1: Demonstrate that the total of all angles made on the same side of a line at a given point of the line is 180°.
The AOB is a linear line and beams OC, OD and OE are placed on it and form ?AOC, ?COD, ?DOE and ?EOB. Proof: ?AOC + ?COD + ?DOE + ?DOE + ?EOB = 180°. ?DOE ?COD + ? + ? + ? + ? = 180°. Thus the total of all angles on the same side of the AB line at a point above the AB line is 180°.
Sentence 2: Show that the total of all angles by one point is 360°. One point M and the beams OA, OB, OC, OD and OE form angles around M. Construction: Together with (i) and (ii) the total of all angles around a point of 360° results.
Sample 1: In the adjacent illustration, AOB is a linear line. Therefore, find ?AOC, ?COD and ?BOD. <font color=#38B0DE>-=?BOD=- Proudly Presents For example 2: In the illustration, OA, OB are opposite beams and ?AOC + ?BOD = 90°. You can find ?COD. Because OA and OB are opposite beams.
Sample 3: In the illustration, OP halved ?BOC and OQ, ?AOC. For example 4: In Fig. 4, OA and OB are opposite beams: Since AOC and BOC make a linear couple, y = 105º. Sample 5: In picture AOC and BOC make a linear couple. As ?AOC and BOC make a linear couple.
?BOD + ?AOC = 90º. You can find ?COD. Because OA and OB are opposite beams. Because beam OE halves angles AOB. For example 8: In illustration OE halved ?AOC, OF halved ?COB and OE ?OF. AOC and COB since OE and OF angles. Therefore, AOC and COB are neighboring angles.
Thus AOC and COB are adjoining complementary angles. So ?AOC and COBRA... make a linear couple. Therefore, OA and OB are two opposite beams. < = 90º. Therefore, example 10: In figure if AOC + BOD = 60º, you will find ?COD.