Jawaban serta pembahasan

Nomor 1

Gambar 1

3a° + 2a° = 90°

5a° = 90°

a = 18°

Gambar 2:

46° + (a + 29°) + (5a + 15)° = 180°

6a° + 90° = 180°

6a° = 90°

a = 15°

Nomor 2

a. m ∠ A dan m ∠ B jika keduanya saling berpelurus

∠A + ∠B = 180°

2/5 ∠ B + ∠ B = 180°

2/5 ∠ B + 5/5 ∠ B = 180°

7/5 ∠ B = 180°

∠B = 180° : 7/5

∠B = 180° × 5/7

∠B = 128,57°

∠A + ∠B = 180°

∠A = 180° – ∠B

∠A = 180° – 128,57°

∠A = 51,43°

Jadi, besar sudut A = 51,43° dan B = 128,57° jika keduanya saling berpelurus.

B. m ∠ A dan m ∠ B jika keduanya saling bepenyiku

∠A + ∠ B = 90°

2/5 ∠ B + ∠ B = 90°

2/5 ∠ B + 5/5 ∠ B = 90°

7/5 ∠ B = 90°

∠B = 90° : 7/5

∠B = 90° × 5/7

∠B = 64,28°

∠A + ∠ B = 90°

∠A = 90° – ∠B

∠A = 90° – 64,28°

∠A = 25,72°

Jadi selisih kedua sudut = ∠ B – ∠ A

= 64,28° – 25,72°

= 38,56°

Nomor 3

A. m∠A – m∠B = 70°

3 m∠B – m∠B = 70°

2 m∠B = 70°

m∠B = 35°

m∠A = 70° + 35° = 105°

m∠A + m∠B = 105° + 35° = 140°

B.

m∠C = 180° – m∠A

m∠C = 180° – 105°

m∠C = 75°

Nomor 4

A. Sudut-sudut sehadap.

∠A₁ = ∠B₁, ∠A₂ = ∠B₂, ∠A₃ = ∠B₃, ∠A₄ = ∠B₄

∠A₁ = ∠D₁, ∠A₂ = ∠D₂, ∠A₃ = ∠D₃, ∠A₄ = ∠D₄

∠B₁ = ∠C₁, ∠B₂ = ∠C₂, ∠B₃ = ∠C₃, ∠B₄ = ∠C₄

∠C₁ = ∠D₁, ∠C₂ = ∠D₂, ∠C₃ = ∠D₃, ∠C₄ = ∠D₄

b. Sudut-sudut sepihak (dalam dan luar).

Jawaban:

∠A₂ = ∠B₁, ∠A₃ = ∠B₄ ∠C₁ = ∠D₂, ∠C₄ = ∠D₃

∠A₃ = ∠D₂, ∠A₄ = ∠D₁ ∠B₃ = ∠C₂, ∠B₄ = ∠C₁

∠A₁ = ∠B₂, ∠A₄ = ∠B₃ ∠A₁ = ∠D₄, ∠A₂ = ∠D₃

∠B₁ = ∠C₄, ∠B₂ = ∠C₃ ∠C₂ = ∠D₁, ∠C₃ = ∠D₄

c. Sudut-sudut berseberangan (dalam dan luar).

Jawaban:

∠A₂ = ∠B₄, ∠A₃ = ∠B₁ ∠B₃ = ∠C₁, ∠B₄ = ∠C₂

∠C₁ = ∠D₃, ∠C₄ = ∠D₂ ∠A₃ = ∠D₁, ∠A₄ = ∠D₂

∠A₁ = ∠B₃, ∠A₄ = ∠B₂ ∠B₂ = ∠C₄, ∠B₁ = ∠C₃

∠C₂ = ∠D₄, ∠C₃ = ∠D₁ ∠A₁ = ∠D₃, ∠A₂ = ∠D₄

Nomor 5

∠ABF + ∠ABC = 180° sudut lurus (180°)

124°+ ∠ABC = 180°

∠ABC = 180° – 124°

∠ABC = 56°

∠ABC dan ∠EAC merupakan dua sudut dalam bersebrangan,

kedua sudut sama besar.

∠ABC = ∠EAC

56° = 2x

2x = 56°

x = 56°/2

x = 28°

Jadi, nilai x adalah 28°.