Question

find the value of y​

Answer 1

Answer:

$y=9$

Step-by-step explanation:

First, let's find the value of x.

Note that the two equations with the x are alternate interior angles. Therefore, their angle measures are equivalent. So, we can write the following equation:

$5x-38=3x-4$

Solve for x. Let's add 38 to both sides:

$5x=3x+34$

Subtract 3x from both sides:

$2x=34$

Divide both sides by 2. So, the value of x is:

$x=17$

We can see that we have a right triangle.

The sum of the three interior angles of a triangle is always 180. Therefore, we can write that:

$90+(7y-20)+(5x-38)=90$

Since we already know that x is 17, substitute 17 for x. This yields:

$90+(7y-20)+(5(17)-38)=180$

Now, we can solve for y. Multiply:

$90+(7y-20)+(85-38)=180$

Combine like terms:

$(7y)+(90-20+85-38)=180$

Evaluate:

$7y+117=180$

Subtract 117 from both sides:

$7y=63$

Divide both sides by 7. So, the value of y is:

$y=9$

And we're done!

Answer 2

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

First you should find out what x is and to do that you should do...

$5x-38=3x-4$

Tip: You should know that those angles are alternate interior and alternate interior angles are equal to each other.

So anyways when you go and solve it you should get...

$5x-38=3x-4\\2x-38=-4\\2x=34\\x=17$

so know that you know what x is I strongly recommend that you plug it in for

$5x-38$ because you will need it soon.

$5x-38\\5(17)-38\\85-38\\47$

Great now that we know the measure of that angle we can finally go and find y.

We can do that by solving for this equation...

$7y-20+47+90=180$

Tip: The sum of all the angles in the triangle is 180.

$7y-20+47+90=180\\7y+117= 180\\7y= 63\\y=9$

So now we are finally done the value of y is 9.