Question

PLEASE HELP DUE TODAY!!!!

Answer 1

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?"