Trigonometry/Exercise: Chasing Angles

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 Worked Example 1: Missing Angle In the diagram above, the two lines marked with arrows are parallel. You are given the angle of 56o and of 115o. Find the angle x. The angle ${\displaystyle \displaystyle \alpha }$ is the same as the 56o angle, since the two lines marked with arrows are parallel and the line that crosses them must cross parallel lines at the same angle. The angle ${\displaystyle \displaystyle \beta }$ is 180o-115o since it and the 115o angle add up to a straight line. So it is 65o. We can now redraw the diagram with the angles as follows: We have a triangle with angles x, 56o and 65o. x+56o+65o=180o. x+121o=180o. x=59o.
 Worked Example 2: Missing Angle in a Star In the diagram above two angles are marked as 75o and one as 101o. Find the angle c. There is an isosceles triangle with angles 75o, 75o and an unknown angle b. So b+75o+75o=180o. b+150o=180o. b=30o. ${\displaystyle \displaystyle \angle BAC=101^{\circ }}$ The angle 'c' is an angle in triangle ${\displaystyle \displaystyle \Delta ABC}$. The other two angles are 30o and 101o. c+30o+101o=180o. c+131o=180o. c= 49o.