Answer:

1.) The sum of the interior angles of a quadrilateral is always 360°, so we can write an equation:

x + (2x+18) + (10x+9) + (13x-5) = 360

Simplifying and solving for x, we get:

26x + 22 = 360

26x = 338

x = 13

To find the smallest angle, we substitute x = 13 into x°:

x° = 13°

To find the largest angle, we substitute x = 13 into (13x-5)°:

(13x-5)° = 164°

Therefore, the value of x is 13, the measure of the smallest angle is 13°, and the measure of the largest angle is 164°.

2.) The sum of the interior angles of an octagon is 1080°. We can write an equation using the given angle measures:

130 + 145 + 155 + 170 + 200 + x + x + 3x = 1080

Simplifying and solving for x, we get:

6x + 700 = 1080

6x = 380

x = 63.33...

The two remaining angles are congruent, so each measures (180 - the sum of the other angle measures) / 2:

(180 - 130 - 145 - 155 - 170 - 200) / 2 = 5

The third angle measures thrice this amount:

3(5) = 15

Therefore, the measures of the remaining angles are approximately 63.33° and 63.33°, and 15°.