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