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sleet_krkn [62]
4 years ago
15

14. Two parallel lines l and m are intersected by a transversal t. If the interior angles on same side of transversal are (2x−8)

o and (3x−7)o . Find the measure of these angles.
Mathematics
1 answer:
nlexa [21]4 years ago
8 0

Answer:

70° and 110°

Step-by-step explanation:

It is given that, two parallel lines l and m are intersected by a transversal t.

The interior angles on same side of transversal are (2x−8)° and (3x−7)°.

We need to find the measure of these angles.

We know that, the sum of interior angles of the same side of the  transversal is equal to 180°. So,

(2x−8)° + (3x−7)° = 180°

⇒ 5x-15=180°

⇒5x=180°+15

⇒5x=195

⇒x=39

Put x = 39 in (2x−8)°,

(2x−8)° = (2(39)-8)°

=70°

Again put x = 39 in (3x−7)°,

(3x−7)° = (3(39)-7)°

=110°

So, the measure of these angles are 70° and 110°.

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Answer:

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Step-by-step explanation:

We need to write the point-slope form of the equation of the line passing through the point (6,-5) and perpendicular to the line y=-\frac{1}{3}x+4

The general form of point-slope is; y-y_1=m(x-x_1)

where m is slope and (x_1,y_1) is the point

We need to calculate slope.

We are given equation of line y=-\frac{1}{3}x+4 that is perpendicular to the required line.

The equation is given in slope-intercept form y=mx+b where m is slope.

Comparing both equations we get m= -1/3

But we know that when lines are perpendicular their slopes are opposite reciprocal of each other i.e m=-\frac{1}{m}

<em>So, </em><em>slope of required line is m = 3 </em><em>(opposite reciprocal of -1/3)</em>

Now, the equation in point-slope form having slope m=3 and point (6,-5) is

y-y_1=m(x-x_1)\\y-(-5)=3(x-6)\\y+5=3(x-6)

So, The equation in point-slope is \mathbf{y+5=3(x-6)}

5 0
3 years ago
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Answer:

1) 1 and 4

2) 1 and 2

3) 1 and 5

4) 2 and 3

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Step-by-step explanation:

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4 0
3 years ago
-3x-y=14<br> 9x- =-27<br><br> Use the method of substitution to solve
eduard

Answer:

The solution to the system of equations is x=3 y= 23  

Step-by-step explanation:

solving this system of equation using substitution method  

 -3x-y=14 …..   equation (1)    

 -9x =-27   ….. equation (2)  

Solving for value of x from equation 2  

-9x =-27    

so x= -27/-9 = 3

so x = 3

The second equation is solved for x, so we can substitute the expression 3 in for x in the first equation (1)

-3x-y=14

-3 (3) - y =14  

-9-y= 14

-9=14+y

y=-23

The solution to the system of equations is x=3 y= -23  

We can check our work by plugging these numbers back into the original equations. Let's try -3x-y=14      

-3x-y=14      

-3(3) -(-23)= 14

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14= 14

Yes, our solution checks out.

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