Soal Garis Dan Sudut Kelas 7 Semester 2 Kurikulum 2013

Soal Latihan Matematika Kelas 7 Semester 2, Bab : Sudut

1.

Pada gambar diatas, tentukan :
a. Nilai x
b. Nilai y
c. Nialai x + y

Pembahasan :
a. 3x + 20 = 5x - 10 (Sudut bertolak belakang)
    5x - 3x = 20 + 10 (3x pindah ke ruas kanan, -10 ke ruas kiri)
    2x = 30
    x = 30 : 2 = 15^o

b. (3x + 20)^o+ (6y + 25)^o = 180^o

     3.15 + 20 + 6y + 25 = 180^o

     45 + 20 + 25 + 6y = 180^o

     6y = 180 - 90 

     y = 90 : 6 = 15^o

c. x + y = 15 + 15 = 30^o

2. 

Pada gambar disamping, tentukan :

a. Nilai x
b. Nilai y
c. Nialai x - y

Pembahasan :
a. 5x - 27 = 73
    5x = 73 + 27
    5x = 100
    x = 100 : 5 = 20^o

b. 5y + 17^o + 73^o = 180^o

    5y = 180 - 90 = 90^o

      y = 90 : 5 = 18^o

   

c. x - y = 20 - 18 = 2^o

3.

Mencari nilai x :
x + 5x + 2x + 4x = 180^o
12x = 180^o
x = 180 : 12 = 15^o

Setelah itu kita bisa tentukan :
<AOB = 15^o
<BOC = 5 . 15 = 75^o
<COD = 2. 15 = 30^o
<DOE = 4. 15 = 60^o

4.

5x + 4x + 9 = 180^o
9x = 180 - 9 = 171^o
  x = 171 : 9 = 19^o
 <PQS = 5. 19 = 95^o
<SQR = 4. 19 + 9 = 85^o

5. 

(3x + 15) + (2x + 10) = 180^o

5x  = 180 - 25 = 155^o
  x = 155 : 5 = 31^o
 <KLN = 3. 31 + 15 = 108^o
<NLM = 2. 31 + 10 = 72^o

6.

4x + 58 + 3x + 73 = 180^o
7x + 131 = 180^o
 7x = 180 - 131 = 49^o
   x = 49 : 7 = 7^o
<ABE = 4. 7 = 28^o
<DBC = 3. 7 + 73 = 94^o
7.

2x + 3x + 85 = 180^o
5x = 180 - 85 = 95^o
  x = 95 : 5 = 19^o
<KON = 2. 19 = 38^o
<NOM= 3. 19 = 57^o

8.

x + 4 + 3x + 6 = 90^o
4x = 90 - 10 = 80^o
  x = 80 : 4 = 20^o
<BOC = 3. 20 + 6 = 66^o
<COD = 20 + 4 = 24^o
<DOE = 2. 20 + 8 = 48^o
<AOE = 180 - (66 + 24 + 48) = 42^o

9.

5x + 10 + 80 + 15x - 20 = 180^o
20x + 70 = 180^o
 20x = 180 - 70 = 110^o
     x = 110 : 20 = 5,5^o
         
5x + 10 = 5. 5,5 + 10 = 37,5^o
15x - 20 = 15. 5,5 - 20 = 62,5^o

10.

2x + 3x + x = 90^o
6x = 90^o
  x = 90 : 6 = 15^o

2x = 2. 15 = 30^o
3x = 3. 15 = 45^o
x = 15 = 15^o



11.

14x + 6x = 90^o
20x = 90^o
  x = 90 : 20 = 4,5^o

14x = 14. 4,5 = 63^o
6x = 6. 4,5 = 27^o

12. 

2x + 5x + 2x = 90^o

9x = 90^o
  x = 90 : 9 = 10^o

2x = 2. 10 = 20^o
5x = 5. 10 = 50^o



13.

b + 37 = 90^o
b = 90 - 37 = 53^o

14.

6x + 4 + 5x + 9 = 90^o
11x + 13 = 90^o
11x = 90 - 13 = 77^o
x = 77 : 11 = 7^o

6x + 4 = 6. 7 + 4 = 46^o
5x + 9 = 5. 7 + 9 = 44^o

15.

6x + 4 + 3x + 5 = 90^o
9x + 9 = 90^o
9x = 90 - 9 = 81^o
x = 81 : 9 = 9^o

6x + 4 = 6. 9 + 4 = 58^o
3x + 5 = 3. 9 + 5 = 32^o

16.

5x + 10 + 30 = 90^o
5x + 40 = 90^o
5x = 90 - 40 = 50^o
x = 50 : 5 = 10^o

5x + 10 = 5. 10 + 10 = 60^o

17. Sudut saling bertolak belakang besarnya sama

<DOB = <AOC = 35^o 
<AOD + <AOC = 180^o
<AOD = <BOC = 180 - 35 = 145^o



18.

2x = 120^o
  x = 120  : 2 = 60^o

5z + 3 = 68^o
5z = 68 - 3 = 65^o
  z = 65 : 5 = 13^o

3y = 42^o
  y = 42  : 3 = 14^o

19.

Mencari Nilai z :
4z + 56 = 108^o
4z = 108 - 56 = 52^o
  z = 52 : 4 = 13^o

Mencari nilai x :
12x + 108 = 180^o
12x = 180 - 108 = 72^o
  x = 72 : 12 = 6^o

Mencari nilai y :
4z + 12x =  5x + 2y
4 . 13 + 12 .  6 =  5 . 6 + 2y
52 + 72 = 30 + 2y
2y = 124 - 30 = 94
  y = 94 : 2 = 47^o

Besar sudutnya :
4z = 4 . 13 = 52^o
12x = 12 . 6 = 72^o
5x + 2y = 5 . 6 + 2 . 47 = 30 + 94 = 124^o


20. 

<FDC dan <FDE saling berpelurus, jadi :
<FDC + <FDE = 180^o
3x + 7x + 80 = 180^o
10x = 180 - 80 = 100^o
    x = 100 : 10 = 10^o

<FCD = 180 - (<FDC + <DFC)
           = 180 - (30 + 25)
           = 180 - 55 = 125^o

<FCB dan <FCD saling berpelurus
<FCB = 180 - <FCD
6y + 7 = 180^o - 125^o
 6y = 55^o - 7^o
   y = 48^o

<ABF = <BFC + <FCB (Sudut luar segitiga)
13x + 5 = 8z + 55^o
13 . 10 + 5 = 8z + 55
8z = 135^o - 55^o
  z = 80^o : 8 = 10^o
<ABC = 135^o
<FBC = 180^o - 135^o = 45^o

21. 

<GAB = <CEF (sudut luar bersebrangan)
<BAE = 180^o - <GAB
      3y =  180^o - 102^o
        y = 78^o : 3 = 26^o





Catatan : tanda . (titik) pada operasi hitung merupakan kali. soalnya ada variabel x, takut rancu.

Semoga Bermanfaat.............