Answer:
Answered below
Explanation:
Sheet 1: Question 3
Vertically opposite angles are equal so you will equate the angles given,
∠LPN = ∠OPM
7 + 13x = -20 + 16x
27 = 3x
x = 9
Sheet 1: Question 4
Vertically opposite angles are equal so you will equate the angles given,
∠ABD = ∠EBC
2x + 20 = 3x + 15
-x = -5
x = 5
Sheet 1: Question 5
Step 1: Find the value of x
Vertically opposite angles are equal so you will equate the angles given,
∠SOP = ∠ROQ
5x = 4x + 10
x = 10
Step 2: Find angles
Angle SOP = 5x = 5(10) = 50°
Angle ROQ = 50° (because it is vertically opposite to angle SOP)
Angle SOR = 180 - 50 (because all angles on a straight line are equal to 180°)
Angle SOR = 130°
Angle POQ = 130° (because it is vertically opposite to angle SOR)
Sheet 1: Question 6
Angle 1 = 72° (because vertically opposite angles)
∠4 + ∠1 + 41 = 180° (because all angles on a straight line are equal to 180°)
∠4 + 72 + 41 = 180
∠4 = 67°
∠3 = 41° (because vertically opposite angles)
∠2 = 67° (because vertically opposite angles)
Sheet 2: Question 3
Step 1: Find the value of x
Sum of complementary angles is equal to 90°
Angle A + Angle B = 90°
7x + 4 + 4x + 9 = 90°
11x = 90 - 13
11x = 77
x = 7
Step 2: Find angle A and angle B using x
Angle A: 7x + 4
7(7) + 4
Angle A = 53°
Angle B: 4x + 9
4(7) + 9
Angle B = 37°
Sheet 3: Question 3
Step 1: Find the value of x
Sum of supplementary angles is equal to 180°.
Angle A + Angle B = 180°
3x - 7 + 2x + 2 = 180°
5x = 185
x = 37
Step 2: Find angle A and angle B using x
Angle A: 3x - 7
3(37)-7
Angle A = 104°
Angle B: 2x + 2
2(37) + 2
Angle B = 76°
Sheet 3: Question 4
Sum of supplementary angles is equal to 180°.
Step 1: Find x
1/4(36x-8) + 1/2(6x-20) = 180°
Take LCM
[36x - 8 + 2(6x - 20)]/4 = 180°
36x - 8 +12x - 40 = 180 x 4
48x - 48 = 720
48x = 768
x = 16
Step 2: Find both angles with the help of x
Angle 1: 1/4(36x-8)
1/4[36(16)-8] = 568/4
Angle 1 = 142°
Angle 2: 1/2(6x-20)
1/2[6(16)-20] = 76/2
Angle 2 = 38°
Sheet 4: Question 1
All angles on a straight line are equal to 180°
Angle z + 138° = 180°
Angle z = 180 - 138
Angle z = 42°
Sheet 4: Question 2
Linear pair 1: 5 and 7 (because both angles are on a straight line and are equal to 180°)
Linear pair 2: 6 and 8 (because both angles are on a straight line and are equal to 180°)
Sheet 4: Question 3
Step 1: Find the value of x
All angles on a straight line are equal to 180° or linear pairs are equal to 180°
Angle LMO + Angle OMN = 180°
7x + 20 + 10 + 5x = 180°
12x = 180 - 30
x = 150/12
x = 12.5
Step 2: Find angles using the value of x
Angle LMO: 7x + 20
7(12.5) + 20
Angle LMO = 107.5°
Angle OMN: 10 + 5x
10 + 5(12.5)
Angle OMN = 72.5°
Sheet 4: Question 4
Linear pairs are equal to 180°.
Angle 1 + Angle 2 = 180°
1/3(27x-6) + 1/2(6x-20) = 180°
Take LCM = 6
[2(27x-6) + 3(6x-20)]/6 = 180
54x - 12 + 18x - 60 = 1080
72x - 72 = 1080
72x = 1152
x = 16
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