Question

Angle Theorems for triangles (20 PTS)

Answer 1

1.
`45^(0)` 2.
`50^(0)` 3.
`30^(0)` 4.
`46^(0)` 5. x =
`59^(0)` 6. w =
`31^(0)` 7. n =
`65^(0)`

Explanation:

1. 45 + 90 + ? = 180

=> ? = 45

2. 60 + 70 + ? = 180

=> ? = 50

3. 85 + 65 + ? = 180

=> ? = 30

4. 104 + 30 + ? = `180

=> ? = 46

5. x + x + (x+3) = 180

=> 3x + 3 = 180

3x = 180 - 3 = 177

x = 177 : 3 = 59

=> angle (x + 3) = 59 + 3 = 62

6. w + w + (4w - 6) = 180

=> 6w - 6 = 180

6w = 180+6 = 186

w = 186 : 6 = 31

=> angle (4w-6) = 4 x 31 - 6 = 118

7. n + n + 50 = 180

=> 2n = 180 - 50

2n = 130

n = 130 : 2 = 65

Answer 2

sum of all the interior angles of the triangles is 180

Explanation:

1)45+90+x=180

x=180-90-45

x=45

2)60+70+x=180

x=180-60-70

x=50

3)85+65+x=180

x=180-85-65

x=30

4)104+30+x=180

x=180-104-30

x=46