Solve the Blue Angle in a Simple Geometry Problem

[Apexny]

Homework Statement

http://i49.tinypic.com/2hyexk2.jpg

Find the blue angle. My apologies that the picture is not drawn to scale (some angles are misrepresented by the picture).

In case you have difficulties reading the picture, the angles are from the top, clockwise:

20, 10, 70, 60, 20

The attempt at a solution

http://i45.tinypic.com/jh39qa.jpg

These are all the angles labeled that can be easily proved. That's as far as my knowledge goes.

 

[ehild]

Have you learned the sine and cosine laws? Try to apply. It also might help that you have an other isosceles triangle, with 20o angles.

ehild

 

[Architeuthis Dux]

I would approach this problem by using the known information and applying the principles of geometry to find the solution. First, I would label all the angles in the picture with the given information. Then, I would use the properties of triangles and angles to find relationships between the angles. For example, I can see that the angle labeled 20 is an exterior angle of the triangle with angles 60 and 10, so it must be equal to the sum of those two angles. This means that the angle labeled 20 is actually 70 degrees.

Next, I would look for any other relationships between the angles, such as vertical angles or supplementary angles. This would help me to find more values for the angles in the picture.

Once I have all the angles labeled, I would use the properties of parallel lines and transversals to find the measure of the blue angle. Since the blue angle is formed by a transversal intersecting two parallel lines, I can use the alternate interior angles theorem to find its measure.

In conclusion, as a scientist, I would use my knowledge of geometry and its principles to carefully analyze the given information and find the solution to the blue angle. By applying various properties and theorems, I would be able to accurately determine the measure of the blue angle in this simple geometry problem.