Answer:
x = -6 and -1
Step-by-step explanation:
x^2 + 6x + 7
Factorise- find two numbers that multiply to be 6 and add to be 7: 6 and 1
(x+6)(x+1)
Set each expression equal to 0 and solve
x + 6 = 0 -> x = -6
x + 1 = 0 -> x = -1
Answer:
see explanation
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 6 ( sides of a hexagon ) , then
sum = 180° × 4 = 720°
(a)
let x be the sixth interior angle , then
90° + 100° + 110° + 120° + 130° + x = 720 , that is
550° + x = 720° ( subtract 550° from both sides )
x = 170°
(b)
the sum of the exterior angles of a polygon is 360°
exterior angle + interior angle = 180°
exterior angle = 180° - interior angle
Then
180° - 90° = 90°
180° - 100° = 80°
180° - 110° = 70°
180° - 120° = 60°
180° - 130° = 50°
180° - 170° = 10°
sum = 90° + 80° + 70° + 60° + 50° + 10° = 360° ← correct total
Answer:
The answer to your question is below
Step-by-step explanation:
1) Alternate interior angles measure the same
10x - 10° = 100°
10x = 100° + 10°
10x = 110°
x = 110° / 10°
x = 11°
2) Alternate exterior angles measure the same
x + 99° = 90°
x = 90° - 99°
x = -9°
3) Supplementary angles measure 180°
(6x + 12) + (14x + 8) = 180°
6x + 12 + 14x + 8 = 180°
20x + 20 = 180
20x = 180 - 20
20x = 160
x = 160 / 20
x = 8
4) Alternate exterior angles measure the same
26x + 1 = 131°
26x = 131° - 1°
26x = 130°
x = 130° / 26°
x = 5
5) Consecutive interior angles measure 180°
x + 100 + 85° = 180°
x + 185 = 180
x = 180 - 185
x = -5
6) Corresponding angles measure the same
7x - 7 = 70
7x = 70 + 7
7x = 77
x = 77 / 7
x = 11
7) Supplementary angles measure 180°
(12x + 8) + (100°) = 180°
12x + 8 + 100 = 180
12x + 108 = 180
12x = 180 - 108
12x = 72
x = 72 / 12
x = 6
8) Consecutive interior angles measure 180°
18x + 8x - 2 = 180°
26x = 180 + 2
26x = 182
x = 182 / 26
x = 7
9) Corresponding angles measure the same
27x + 7 = 28x + 3
27x - 28x = 3 - 7
-1x = -4
x = -4/-1
x = 4
10) Consecutive interior angles measure 180°
(x + 107) + (x + 87) = 180
x + 107 + x + 87 = 180
2x + 194 = 180
2x = 180 - 194
2x = -14
x = -14 / 2
x = -7
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