2 Simple Lines

Perpendicular lines are negative recipricols of eachother.

The two slopes given are -2 an 1/2. Since they multiply together to -1, then they are perpendicular and the angle between them is 90°.

Actually in the figure 4 squares of equal sides are joined together. And both of the bold lines are equal to each other. Hence by right angle triangle are congruent, also the angle of both triangles will be same then by the angle sum property answer comes to be 90*

Using angle sum property of a triangle is the best and simple way to work out this sum!!

Assign each unit square to be 1x1 units. Therefore, using simple inverse trigonometry, we use the equation $\arctan { \frac { 1 }{ 2 } }$ This yields around 26 degrees. Using the triangle angle sum rule, we find that the other angle is equal to 180-26-90= 64 degrees. Now that we have defined the angles of this triangle, we identify that the shape outside these two triangles, a quadrilateral, which angles are the unknown blue, the angle supplementary to 26 degrees, a right angle, and the angle complementary to 64 degrees. Therefore, since the sum of a quadrilateral's angles are 360, we can easily calculate the unknown length. 360-(90-26)-90-(180-64)= 90. The unknown angle is 90 degrees.