In the figure, ∠4 is an exterior angle to ∠aul.

In the figure, ∠4 is an exterior angle to AUL.

∠4 =  77°

∠4 = ∠1 +∠2

∠1 +∠2 = 52° +25° = 77°

Substitute the value that we alreay know to find ∠3.

⇒ 77° + ∠3 = 180°

⇒ ∠3 = 180° - 77° = 103°

∠4 is equal to the measures of two nonadjacent interior angles, the sum of angles is always 180° so ∠1 +∠2 + ∠3 = 180°. In summary ∠4=sum of the measures of the two nonadjacent interior angles.

Hope this helps, have a BLESSED AND WONDERFUL DAY! As well as a great Valentine's day! :-)

- Cutiepatutie ☺❀❤

9514 1404 393

  obtuse

Step-by-step explanation:

Using the idea of a "form factor", we find ...

  f = a² + b² - c²

  f = 25² +30² -50² = 625 +900 -2500 = -975

The form factor is negative, so the triangle is obtuse.

_____

Additional comment

The form factor, as defined above, classifies the triangle according to its sign:

  f > 0 . . . acute

  f = 0 . . . right

  f < 0 . . . obtuse

The largest angle in the triangle can be found from ...

  cos(C) = f/(2ab)

Here, it is C = arccos(-975/1500) ≈ 130.5416°