Triangle sum and exterior angle theorem. find the x
please help i’m really bad at this and don’t understand!!

The value of x in triangle 1 is 75 degrees

The value of x in triangle 2 is 63 degrees

The value of x in triangle 3 is 20 degrees

The value of x in triangle 4 is 55 degrees

The value of x in triangle 5 is 23 degrees

The value of x in triangle 6 is 17 degrees

The value of x in triangle 7 is 85 degrees

The value of x in triangle 8 is 30 degrees

The value of x in triangle 9 is 147 degrees

The value of x in triangle 10 is 29 degrees

The value of x in triangle 11 is 60 degrees

The value of x in triangle 12 is 27 degrees

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The sum of two opposite interior angles is equal to the external angle.

Types of triangles

Triangle 1: 180 - (58 + 47) = 75 degree

Triangle 2: 180 - 96 - 21 = 63 degrees

Triangle 3: 180 =  (3x - 1 + 31 + 90)

180 = 120 +  3x

180 - 120 = 3x

60 = 3x

x = 20 degrees

Triangle 4: 21 + 34 = 55 degrees

Triangle 5: 100 = 2x + 3 + 51

100 = 2x + 54

100 - 54 = 2x

46 = 2x

x = 23 degrees

Triangle 6: 94 = 60 + 2x

94 - 60 = 2x

34 = 2x

x = 17 degrees

Triangle 7: 180 - 52 - 43 = 85 degrees

Triangle 8: x + 2x + 3x = 180

6x = 180

x = 30 degrees

Triangle 9: 2x - 2 + x + 5 = 90

3x + 3 = 90

3x = 90 - 3

3x = 87

x = 29 degrees

Triangle 10: 180 - 10 - 23 = 147 degrees

Triangle 11: 180 =  x +  x + x

180 = 3x

x = 60 degrees

Triangle 12: 180 = 3x - 17 + x + 40 + 2x - 5

180 = 6x + 18

180 - 18 = 6x

162 = 6x

x = 27 degrees

To learn more about triangles, please check: link

Did two of them for you as reference for the rest.

Explanation for #1

The sum of all the angles in a triangle is 180. Simply add the given angles. Take 180 and subtract the sum of the given angles

180 - (58 + 47) = 75

Missing angle is 75

Explanation for #4

A straight angle is 180 degrees. Same thing as the first: add the given angles then take 180 and subtract it.

Then take 180 again and subtract the answer you got from the first step.

180 - (21 + 34) = 125

180 - 125 = 55

The missing angle is 55

d

step-by-step explanation:

d