Use e figure below to find the value of y and each angle shown.


Use e figure below to find the value of y and each angle shown.

Answers

x = 5AB = 16BC = 15AC = 31

Step-by-step explanation:

The segment addition theorem tells you ...

  AB + BC = AC

Filling in the expressions for these segments, you have ...

  (3x +1) + (4x -5) = (8x -9)

  3x +1 +4x -5 +9 -7x = 8x -9 +9 -7x . . . add 9 - 7x to both sides of the equation

  5 = x . . . . . . . simplify

__

AB = 3·5 +1 = 16

BC = 4·5 -5 = 15

AC = 8·5 -9 = 31

Sum of interior angles in a triangle = 180

2x - 1 + 11x + 3 + 5(x - 4) = 180

13x + 2 + 5x - 20 = 180

18x - 18 = 180

18x = 198

  x = 11

x=4, y=8

Step-by-step explanation:

step 1

Find the value of y

we know that

In the right triangle of the figure

cos(30\°)=\frac{4\sqrt{3}}{y}

Remember that

cos(30\°)=\frac{\sqrt{3}}{2}

so

\frac{\sqrt{3}}{2}=\frac{4\sqrt{3}}{y}

Simplify

y=8\ units

step 2

Find the value of x

In the right triangle of the figure

sin(30\°)=\frac{x}{8}

Remember that

sin(30\°)=\frac{1}{2}

so

\frac{1}{2}=\frac{x}{8}

x=4\ units

5y - 16 + 3y + 20 = 180 degrees

Combine like terms on the left side

8y + 4 = 180

Subtract 4 from both sides.

8y = 176

Divide both sides by 8

y = 22

Plug 22 into y for each angle.

3y + 20 = 3(22) + 20 = 66 + 20 = 86 degrees

5y - 16 = 5(22) - 16 = 110 - 16 = 94

The angle opposite 5y - 16 also equals 94 because they are vertical angles.

The angle opposite of 3y + 20 also equals 86 because they are vertical angles

Step-by-step explanation:

Providing you are working with 2 straight lines that intersect, the 2 given angles are supplementary.

3y+20 + 5y - 16 = 180            Collect like terms

8y + 4 = 180                            Subtract 4 from both sides

8y + 4-4=180-4                       Collect like terms

8y = 176                                  Divide by 8

8y/8 = 176/8

y = 22

Angle 1

3y + 20

3*22 + 20

66 + 20

86

Angle 2

5y - 16

5*22 - 16

110 - 16

94

22,86,94

 B

22, 86 , 94

Step-by-step explanation:

the measure of angle of a line is 180°

to find value of y..

3y + 20 + 5y - 16 = 180

3y + 5y = 180 - 20 + 16

8y = 176

y = 176/8

y = 22

and the measure of angles..

3*22 + 20 = 86

5*22 - 16 = 94

and.. 94+86 = 180

so y = 22 and angles are 86° and 94°



Do you know the answer?

Other questions on the subject: Mathematics

Mathematics, 21.06.2019, kevinsosdik
one set of data has more variation than the other. hope this !...Read More
1 more answers
Mathematics, 21.06.2019, bhebert6057
Domain: [1,2,3,...9460]Range: [45.50, 91, 136.5...430430]Step-by-step explanation:Let the number of people in attendance at a game =xEach ticket costs $45.50.Therefore, Revenue, f(...Read More
1 more answers
Mathematics, 21.06.2019, piyonax
answer: need picture of problem step-by-step explanation:...Read More
1 more answers
Mathematics, 21.06.2019, sjsmith21
for apex Probability if hitting a home run given that you didn’t strike out Step-by-step explanation:...Read More
3 more answers