One of the outer corners of a right-angled triangle is 140º. What is the inside acute angle of a right-angled

One of the outer corners of a right-angled triangle is 140º. What is the inside acute angle of a right-angled triangle that is not adjacent to the given outside angle?

It is known from the condition that one of the outer corners of a right-angled triangle is 140º.

In order to find what the inner acute angle of a right-angled triangle is equal to, which is not adjacent to a given outer angle, let’s recall the property of adjacent angles and the theorem on the sum of the inner angles of a triangle.

So, the sum of adjacent angles is 180 °.

Now we can find the corner of the triangle adjacent to the outer corner.

180 ° – 140 ° = 40 °.

The sum of the angles of a triangle is 180 ° (sum of angles theorem).

180 ° – (90 ° + 40 °) = 180 ° – 130 ° = 50 °.

Answer: 50 °.