In a triangle, one of the angles is 35 ° and the other 70 °. Find the value of the vertex angle built at the top of the third corner?

Given:
∆ABC
∠А = 35 °
∠С = 70 °
To find:
External ∠AВН
Decision:
First, you need to draw ∆ABС, and then extend the BC side beyond the triangle. We got another angle, let’s call it ∠AВН.

1) Consider ∆ABС:
∠А + ∠В + ∠С = 180 °
35 ° + ∠В + 70 ° = 180 °
∠B + 105 ° = 180 °
∠B = 180 ° -105 ° (the sign changes with transfer)
∠В = 75 °

2) ∠НВА and ∠ABС are adjacent =⟩ the sum of these angles 180 ° (by the theorem on adjacent angles) =⟩
∠НВА = 180 ° -75 °
∠НВА = 105 °

Answer: ∠НВА = 105 °