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9514 1404 393
Answer:
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 ...
- corresponding angles are congruent (at a transversal of parallel lines)
- alternate interior angles are congruent
- an exterior angle equals the sum of remote interior angles
- acute angles in a right triangle are complementary
- angles in a triangle sum to 180°
- linear pair angles are supplementary
- angle sum theorem
