When two parallel lines are intersected by a transverse line, they form eight angles. You can consider the parallel lines as the horizontal lines of the letter Z and the transversal as the sloped line of Z. Then the two angles in that Z-shape are the Z angles. The transversal for Z-angles can slope either way.
It can be proved that Z-angles, properly called ALTERNATE angles, are equal.
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An 'F' angle is called a corresponding angle, a 'Z' angle is called an alternate angle and a 'C' angle is called a supplementary angle.
Let the sides be x y z and their opposite angles be X Y Z Using the cosine rule angle X = 41 degrees Using the cosine rule angle Y = 115 degrees Angle Z: 180-41-115 = 24 degrees
Very simple, let's mount a linear system: x=measure of the angle; y=supplement; z=complement: I:x+y= 180; II:x+z= 90; III: y+z= 150; Summing I with II we have: I+II: 2x+y+z= 270; III: y+z=150 Now, subtracting III from I+II we have a simple equation: 2x=120; >x= 60< So, the angle whose sum of the measures of its complements and supplement is 150, has 60 degrees.
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Oh, what a happy little question! To put arcsec in a calculator, you simply press the "2nd" or "Shift" key on your calculator, then find the "sec" button. This will allow you to calculate the arcsec of an angle and create beautiful mathematical landscapes. Just remember, there are no mistakes, only happy little calculations!