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Let's first deal with the angles towards the top of the diagram. You should immediately notice that angle H is opposite the right angle and therefore angle H has a value of 90 degrees.
Now that will mean that the sum of the angles that are listed as (8m - 18) and (5p + 2) will add up to 90. And since the angle (7m + 3) is opposite to the (5p + 2) angle, they're equal. Therefore (8m - 18) + (7m +3) = 90. Let's see what m is
(8m - 18) + (7m +3) = 90
8m - 18 + 7m + 3 = 90
15m - 15 = 90
15m = 105
m = 7

Since m = 7, you immediately know that (8m - 18) = 38, and (7m + 3) = 52.
And because of the opposite angles, you also know that (5p + 2) = 52, so p = 10, and (11t - 17) = 38, so t = 5

The line CE has been divided into 2 equal halves by point D, so
5a + 12 = 9a - 12

Solving for a, gets
5a + 12 = 9a - 12
12 = 4a - 12
24 = 4a
6 = a

So a = 6

The two angles off of point E are marked as congruent, so
48 = 21s + 6
42 = 21s
2 = s

So s = 2.

Now let's arrange the variables in numeric order.
s = 2
t = 5
a = 6
m = 7
p = 10

And upon doing so I see the word "stamp" as the answer to the riddle "What sits in a corner but travels around the world?"

Simultaneous equations can be solved if the number of unknown variables are equal to the number of equations. In the geometry question, the equations are given by the relationship between the lines and angles

Part A

m = 7°, p = 10°, t = 5°, a = 6, and s = 2°

Part B

Arranging the variables from least to greatest gives; stamp

A stamp sits at the corner of an envelope but travels around the world

Part A

From the diagram, we have;

H is a vertical angle to the 90° angle

(7·m + 3)° + 90° + (8·m - 18)° = 180° (linear angles)

∴ (7·m + 3)° + (8·m - 18)°  = 180° - 90° = 90°

(15·m - 15)° = 90°

15·m = 90°+ 15° = 105°

m = 105°/15 = 7°

m = 7°

(7·m + 3)° = (5·p + 2)° (vertically opposite angle theorem)

∴ (5·p + 2)° = (7 × 7 + 3)° = 52°

p = (52° - 2°)/5 = 10°

p = 10°

(8·m - 18)° = (11·t - 17)° (vertically opposite angle theorem)

∴ (8 × 7 - 18)° = (11·t - 17)°

38° = (11·t - 17)°

11·t = 38° + 17° = 55°

t = 55°/11 = 5°

t = 5°

CD = 5·a + 12 and DE = 9·a - 12 are congruent segments

5·a + 12 = 9·a - 12 (Definition of congruent segments)

9·a - 5·a = 12 + 12 = 24

4·a = 24

a = 24/4 = 6

a = 6

(21·s + 6° and 48° are congruent congruent angles

21·s + 6° = 48° (Definition of congruent angles)

∴ s = (48° - 6°)/21 = 2°

s = 2°

Part B

Arranging the values of the variables from least to most gives;

s = 2°

t = 5°

a = 6

m = 7°

p = 10°

Which gives;

The answer to the riddle = s, t, a, m, p = Stamp

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