Let's see the remarkable property that connects three angles of a triangle.
The sum of the measure of three angles of a triangle is 180°.
Consider a triangle \(ABC\) with interior angles measures \(∠1\), \(∠2\) and \(∠3\). Draw a line \(DE\) parallel to \(BC\).
Now the angle formed by the parallel line \(DE\) with the triangle \(ABC\) is \(∠4\) and \(∠5\).
Since \(DE\) is parallel to \(BC\), using the alternate interior angle property \(∠2\) must equal to \(∠4\).
Similarly, \(∠3\) must be equal to \(∠5\).
That is \(∠2 = ∠4\) and \(∠3 =∠5\).
As \(DE\) is a straight line, \(∠5\) and \(∠CAD\) are linear pairs (Pair of adjacent supplementary angles).
\(∠5 + ∠CAD = 180°\)
That is, \(∠5 + ∠1 + ∠4 = 180°\)
Equivalently, \(∠1 + ∠2 + ∠3 = 180°\).
It states that the total measures of the three angles of a triangle is \(180°\).