Today in class students worked to find the pattern that when you create triangles, the sum of the shorter sides is greater than the long (hypotenuse) side. All interior angles of a triangle still add up to 180 degrees.
Answers to HW: Complementary angles: two angle measures that add up to 90 degrees Supplementary angles: two angle measures that add up to 180 degrees Vertical angles: opposite angles formed when two lines cross; equal in degree measure m< 1 = 120 degrees (given) m< 2 = 60 degrees (supplementary to angle 1) m< 3 = 120 degrees (vertical to given angle 1) m< 4 = 60 degrees (vertical to angle 2, or supplementary to angle 3 or 1) Yes there are different ways to see the vertical and supplementary angles to solve for the unknowns. Angle MAX + Angle SAM = 118 65 + x = 118 x = 53 Angle PMT is a right angle as indicated by the box; 90 degrees Angle PMA is given as = 68 degrees Angle MPA is given as = 48 degrees Angle PAM must be 64 degrees because 180 degrees (all three angles) = 68 (<PMT) + 48 (<MPA) + x Angle AMT must be 22 degrees because 90 degrees = 68 (<PMT) + x Angle MAT must be 116 degrees because 180 degrees (supplementary) = 64 (<PAM) + x Angle ATM must be 68 degrees because 180 degrees (all three angles) = 22 (<AMT) + 116 (<MAT) + x The other 2 angles, without a third identifying point, are identified because of their vertical angle equivalents as 116 degrees and 64 degrees 90 degrees - 70 degrees = 20 degrees (complementary rule) 180 degrees - 45 degrees = 135 degrees (supplementary rule)
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