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Straight lines:
Lenku_veidi_1taisne.png
The angle ∡AOB=180°  is a wide-angle, and a beam \(OC\) divides it into two parts then ∡1+∡2=180°.
The sum of two angles on a straight line is 180°, such angles are called Supplementary angles.
When two angles are supplementary, each angle is said to be the supplement of the other.
Example:
45.svg

∠AOB  and ∠BOC - adjacent angles

∠AOB  + ∠BOC  = ∠AOC .

∠AOC  and ∠COP- linear pair.
Therefore, their sum is 180°  (∠AOC  + ∠COP  = 180°).
Combining these two results we get ∠AOB  + ∠BOC  + ∠COP  = 180°.
Thus, the sum of all the angles formed at a point on a straight line is 180°.
Intersecting lines:
Lenku_veidi_2taisnes.png
If two lines intersect, then two pairs of vertical angles are formed ∡1,∡3 and ∡2,∡4.
 
∡1+∡2=180° and ∡1+∡4=180°  by the property of adjacent angles, therefore, ∡2=∡4.
 
It is also clear that ∡1=∡3.
Vertical angles are equal.
Perpendicular lines and angles formed by them
If one of the vertical angles of the line is equal to 90°, then the remaining angles are also straight.
If two intersecting straight lines form four right angles, they are called perpendicular.
Lenku_veidi_taisne_perp.png
It has written down a⊥b.
Two straight lines, perpendicular to the third, do not intersect.
Lenku_veidi_2taisnes_perp.png