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CaHeK987 [17]
3 years ago
6

Find the measure of each numbered angle

Mathematics
2 answers:
snow_tiger [21]3 years ago
8 0

Answer:

\angle 1 =123^{\circ}

Step-by-step explanation:

Given : \angle 2 = 57

To Find : \angle 1 = ?

Solution:

Linear pair : A linear pair is a pair of adjacent, supplementary angles.

So, \angle 1 +\angle 2 = 180^{\circ}

\angle 1 +57^{\circ}= 180^{\circ}

\angle 1 = 180^{\circ}-57^{\circ}

\angle 1 = 180^{\circ}-57^{\circ}

\angle 1 =123^{\circ}

Hence \angle 1 =123^{\circ}

yulyashka [42]3 years ago
7 0

<1 + <2 =180  it is a straight line

<1 + 57 =180

subtract 57 from both sides

<1=180 -57

<1 = 123 degrees

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the sum of three numbers is 79. The second number is 5 times the first, while the third is 16 more than the first. Find the numb
swat32
Let the 1st number be x; 2nd number be y; 3rd number be z.

x + y + z = 79

x = number we are looking for.
y = x * 5 ==> 5 times the first
z = x + 16 ==> 16 more than the first

Therefor,

x + (x * 5) + (x+16) = 79

1st step, multiply the 2nd number: x * 5 = 5x

x + 5x + x + 16 = 79

Add all like numbers:

7x + 16 = 79

To get x, transfer 16 to the other side and change its sign from positive to negative.

7x = 79 - 16
7x = 63

To get x, divide both sides by 7

7x/7 = 63/7
x = 9

To check. Substitute x by 9.

x + (x * 5) + (x+16) = 79

9 + (9 * 5) + (9 + 16) = 79
9 + 45 + 25 = 79
79 = 79 equal. value of x is correct.

3 0
4 years ago
What set of reflections would carry rectangle ABCD onto itself?
Dvinal [7]

Answer:

  y=x, x-axis, y=x, y-axis

Explanation:

Reflecting the figure across three axes just moves it from one quadrant to another. It does not map the figure to itself.

Reflecting across the line y=x moves it from quadrant II to IV or vice-versa. If it is in quadrant I or III, it stays there. So the sequence of reflections x-axis (moves from I to IV), y=x (moves from IV to II), x-axis (moves from II to III), y=x (stays in III) will not map the figure to itself.

However, the last selection will map the figure to itself. The initial (and final) figure location, and the intermediate reflections are shown in the attached. The figure starts and ends as blue, is reflected across y=x to green, across x-axis to orange, across y=x to red, and finally across y-axis to blue again.

7 0
4 years ago
Find the probability of rolling two number cubes and getting a 2 on the first number cube and a 6 on the second?
Tanzania [10]

Answer:

A

Step-by-step explanation:

A cube has 6 sides

Only one side of the cube has 2 on it

The probability of getting 2 would be 1/6

Only one side of the cube has 6 on it

The probability of getting 6 would be 1/6

For both events to happen together

1/6 x 1/6 = 1/36

4 0
3 years ago
Solve each given equation and show your work. Tell wether it has one solution, an infinite number of solutions, or no solutions,
3241004551 [841]

Answer:

See below in bold.

Step-by-step explanation:

(A) 20 -4x=12 -x+8-3x

-4x + x + 3x = 12 + 8 - 20

0 = 0  This is an Identity.

Infinite solutions.

B). 5x+4x-3=24+8x

9x - 8x = 24 + 3

x = 27.  One solution.

C.  5x+6=2x+6+3x-15

5x - 2x - 3x  = -15 + 6 - 6

0 = -15

No solution.

3 0
4 years ago
write an equations in slope-intercept form of the line that passes through the point(5,9) with slope 7
vovangra [49]

Answer:

y=7x-26

Step-by-step explanation:

1) Write it in the slope-intercept form of y=mx+b, where m is the slope and b is the y-intercept.

y=7x +c

2) Substitute the given coordinates into y=7x +b, and then solve for c.

9=7(5) +b\\9=35+b\\9-35=b\\b= -26

3) Substitute c into y=7x +b

y=7x-26

Therefore, the answer is y=7x-26.

6 0
2 years ago
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