Gina Wilson all things algebra unit 4 homework 3 questions 12-15

Step-by-step explanation:

the essential thing to remember here (and please, burn this into your brain for life) : the sum of all angles in a triangle is always (really always) 180 degrees.

therefore, in 12 and 13 we only need to add all 3 angles, and their sum must be 180.

from there we get really all 4 answers.

the next thing to consider is when a triangle had two equal angles, then it is an isoceles triangle (the 2 sides leading away from these 2 angles are equally long). that gives us the answers for 14 and 15.

12.

3x + 18 + 7x - 58 + 2x - 8 = 180

12x - 48 = 180

12x = 228

x = 19

angle A = 3x+18 = 3×19 + 18 = 57+18 = 75 degrees

angle B = 7x-58 = 7×19 - 58 = 133-58 = 75 degrees

angle C = 2x-8 = 2×19 - 8 = 38 - 8 = 30 degrees

13.

8x - 17 + 19x + 4 + 5x + 1 = 180

32x - 12 = 180

32x = 192

x = 6

angle Q = 8x-17 = 8×6 - 17 = 48-17 = 31 degrees

angle R = 19x+4 = 19×6 + 4 = 114+4 = 118 degrees

angle S = 5x+1 = 5×6 + 1 = 30+1 = 31 degrees

14.

KL = 9x - 14

LM = 7x - 37

KM = 3x + 23

angle K = angle L

so, the sides LM and KM must be equally long. that gives us

7x - 37 = 3x + 23

4x = 60

x = 15

KL = 9x-14 = 9×15 - 14 = 135-14 = 121

LM = 7x-37 = 7×15 - 37 = 105-37 = 68

KM = 3x+23 = 3×15 + 23 = 45+23 = 68

15.

XY = 13x - 21

YZ = 8x - 6

XZ = x + 4

angle X = angle Z

so, the sides XY and ZY (or YZ) must be equally long. that gives us

13x - 21 = 8x - 6

5x = 15

x = 3

XY = 13x-21 = 13×3 - 21 = 39-21 = 18

YZ = 8x-6 = 8×3 - 6 = 24-6 = 18

XZ = x + 4 = 3+4 = 7

idk

step-by-step explanation:

your victory is right around the corner. never give up.

- niki minaj

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.