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3 years ago

M<1 = 95 and m<2 =36: What is m<7? Answers and figure attached!

Mathematics

1 answer:

iren [92.7K]3 years ago

4 0

∠7 = 59°

∠6 = ∠2 = 36° ( vertical angles )

∠4 = 180° - ∠1 ( straight angle )

∠4 = 180° - 95° = 85°

∠7 = 180° - (85 + 36 )° ( sum of angles in a triangle )

∠7 = 180° - 121° = 59°

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The measure of two opposite interior angles of a triangle are and. The exterior angle of the0x−14x+4triangle measures. Solve for

11111nata11111 [884]

Answer:

60 degrees

Step-by-step explanation:

Restructured question:

The measure of two opposite interior angles of a triangle are x−14 and x+4. The exterior angle of the triangle measures 3x-45 . Solve for the measure of the exterior angle.

First you must know that the sum of interior angle of a triangle is equal to the exterior angle

Interior angles = x−14 and x+4

Sum of interior angles = x-14 + x + 4

Sum of interior angles = 2x - 10

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Equating both:

2x - 10 = 3x - 45

Collect like terms;

2x - 3x = -45 + 10

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Get the exterior angle:

Exterior angle = 3x - 45

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Hence the measure of the exterior angle is 60 degrees

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3 years ago

Help me answer these PLEASE ASAP

Hoochie [10]

Answer:

Answered below

Step-by-step 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

7 0

3 years ago