Fig.1 |

Let ABC is a triangle whose three angles are ∠A = x°, ∠B = y° and ∠C = z°

We have to prove *x° + y° + z° = 180°*

**Construction : **

**
**Three sides AB, BC, and AC are extended in both the directions. Then a line RAS is drawn from point A in such a way that RAS॥PQ.

Fig.2 |

**Proof: ** ∵ RAS॥PQ and MN is transversal ( According to the construction )

∴ ∠CBA = ∠NAS = y°

Similarly, ∠BCA = ∠TAR = z°

Now, at point A, ∠SAC = ∠TAR = z° ( vertical opposite angles ) and

∠RAB = ∠NAS = y° ( vertical opposite angles )

Now, At the point A, ∠RAS = 180° ( straight angle )

⇒ ∠RAB + ∠BAC + ∠SAC = 180°

⇒ y° + x° + z° = 180°

∴ ** **x° + y° + z° = 180°

*(Proved)***For more details click on the video below.**