Use all of the angle relationships that we have covered to find the missing angles in the puzzle below Based on the puzzle, what is the measure of each of the following angles?

choices:
48
125
37
143
84
96
26
111
69
34
58
169
62
53
128

9514 1404 393

  see attached

Step-by-step explanation:

I started with triangle GHJ on the right. It is isosceles, so ...

  g = 48°

  h = 2(90 -g) = 84°

  k = 180° -h = 96°

Then, on the lower right, we have ...

  a = 180° -143° = 37°

  b = 143°

  c = e = a = 37°

  f = 90° -e = 53°

At vertex D, we also have ...

  85° +d = b  ⇒  d = 143° -85° = 58°

In triangle DGH, we have ...

  m + d = h  ⇒  m = h -d = 84° -58° = 26°

The sum of angles in triangle DGP is 180°, so ...

  p = 180° -85° -26° = 69°

Finally, ...

  s = p = 69°

  r = 180° -p = 111°

_____

The relationships we used are ...

step-by-step explanation:

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