Question

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​

Answer 1

9514 1404 393

Answer:

see attached

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