Question

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Answer 1

Answer:

x is 20

and

y is 9

Step-by-step explanation:

i hope this will help you

Answer 2

Answer

In the given diagram, we have two lines which are parallel to each other and a transversal line passing through them. We are given with two different variables to find the values of those. First, we'll find the value of x.

We know that the vertically opposite angles measures same. So,

Value of ∠x :

$\sf \dashrightarrow 162 - 4x = 5x - 18$

$\sf \dashrightarrow 162 + 18 = 5x + 4x$

$\sf \dashrightarrow 180 = 9x$

$\sf \dashrightarrow 9x = 180$

$\sf \dashrightarrow x = \dfrac{180}{9}$

$\sf \dashrightarrow x = 20$

Now, to find the value of y, we should know that value of the other angle which is given in the same side of the transversal. So, let's find out the value of that angle as we know the value of x.

$\sf \dashrightarrow 162 - 4x$

$\sf \dashrightarrow 162 - 4(20)$

$\sf \dashrightarrow 162 - 80$

$\sf \dashrightarrow {82}^{\circ}$

Now, we can find the value of y.

$\sf \dashrightarrow 7y + 19 = 82$

$\sf \dashrightarrow 7y = 82 - 19$

$\sf \dashrightarrow 7y = 63$

$\sf \dashrightarrow y = \dfrac{63}{7}$

$\sf \dashrightarrow y = 9$

Hence, the values of x and y are 20 and 9 respectively.