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In Geometry, angles have relationships based on their positioning and total measure. Key concepts include complementary, supplementary, vertical, adjacent angles, and linear pairs. These are essential in understanding Geometry basics.
While I can't provide direct answers to your homework, I can certainly guide you on the concept of angle relationships which is essential in understanding your Unit 1 Geometry basics homework.
In Geometry, certain angles have relationships with each other, particularly when they share common characteristics. Some of the important ones include:
Understanding these relationships, and knowing that the sum of angles in a triangle is 180 degrees, should help in solving related problems. Good luck with your homework!
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Answer:
Step-by-step explanation:
1) x + 65 = 90
x = 90 -65
x = 25
2) x + 51 = 180 {Linear Pair}
x = 180 - 51
x = 129
3) y = 107 {Vertically opposite angles are equal}
x + 107 = 180 {linear pair}
x = 180 - 107
x = 73
z = x {Vertically opposite angles are equal}
z = 73
4) If sum of two angles is 180,, then they are called supplementary.
one angle = 13
It's supplement = 180 - 13
= 167
5) If sum of two angles is 90, then they are called complementary.
one angle = 38
It's complement = 90 - 38
= 52
6) ∠1 + ∠2 = 180
5x + 9 + 3x +11 = 180 {Combine like terms}
8x + 20 = 180
8x = 180 -20
8x = 160
x= 160/8
x = 20
∠1 = 5x + 9
= 5*20 +9
= 100+9
= 109
∠2 = 3x +11
= 3*20 +11
= 60 +11
= 71
7) Vertically opposite angles are equal
∠2 = ∠2 1
20x - 14 = 17x + 1
20x - 17x -14 = 1
3x - 14 = 1
3x =1 +14
3x = 15
x = 15/3
x = 5
∠2 = 20x - 14
= 20*5 - 14
= 100 - 14
= 86
8) ∠K + ∠L = 90
3x +3 + 10x - 4 = 90 {Combine like terms}
13x -1 = 90
13x = 90 + 1
x = 91/13
x = 7
∠K = 3x + 3
= 3*7 + 3
= 21 +3
= 24
∠L = 10x - 4
= 10*7 -4
= 70 - 4
= 66
