Triangle 1 has an angle of 55 degrees and 1 of the outer ones is 105 degrees, find all the angles.

It is known from the condition that in a triangle one of the inner angles is 55 °, and one of the outer angles is 105 °. In order to find the remaining interior angles of a triangle, we recall what the sum of adjacent angles and the theorem on the sum of the angles of a triangle are equal to.

So, the sum of adjacent angles is 180 °. Based on this, we can find the angle of the triangle adjacent to the outer one at 105 °.

180 ° – 105 ° = 75 ° an angle of a triangle adjacent to an angle of 105 °.

We know the two corners of the triangle.

From the theorem on the sum of the angles of a triangle, we know that the sum of the angles of a triangle is 180 °.

Looking for the third corner:

180 ° – (55 ° + 75 °) = 180 ° – 130 ° = 50 °.