### Theory:

Straight lines: The angle $\measuredangle \mathit{AOB}\phantom{\rule{0.147em}{0ex}}=180\mathrm{°}$  is a wide-angle, and a beam $$OC$$ divides it into two parts then $\measuredangle 1+\measuredangle 2=180\mathrm{°}$.
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: 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: If two lines intersect, then two pairs of vertical angles are formed $\measuredangle 1,\measuredangle 3$ and $\measuredangle 2\phantom{\rule{0.147em}{0ex}},\measuredangle 4$.

$\measuredangle 1+\measuredangle 2=180\mathrm{°}$ and $\measuredangle 1+\measuredangle 4=180\mathrm{°}$  by the property of adjacent angles, therefore, $\measuredangle 2=\measuredangle 4$.

It is also clear that $\measuredangle 1=\measuredangle 3$.
Vertical angles are equal.
Perpendicular lines and angles formed by them
If one of the vertical angles of the line is equal to $90\mathrm{°}$, then the remaining angles are also straight.
If two intersecting straight lines form four right angles, they are called perpendicular. It has written down $a\perp b$.
Two straight lines, perpendicular to the third, do not intersect. 