Question

The question is below:​

Answer 1

`x=19.5^o`

`\angle RQS=43^o`

Explanation:

Notice that the addition of these two angles give you and angle of
`180^o`, therefore we can write the following equation to represent such addition:

`(2x+4)^o + (6x+20)^o=180^o\\2x+6x+4^o+20^o=180^o\\8\,x+24^o=180^o\\8\,x=180^o-24^o\\8\,x=156^o\\x=156^o/8\\x=19.5^o`

Therefore, the value of the angle RQS is:

`\angle RQS=(2\,x+4)^o=(2\,*\,19.5^o)+4^o=43^o`

Answer 2

x = 19.5, RQS=43

Explanation:

It is important to note that RQS and TQS are supplementary, meaning their angles will add up to 180. Knowing this, we can create and solve the equation to find x..

(2x+4) + (6x+20) = 180

8x + 24 = 180

8x = 156

x = 19.5

Now that we know the value of x, we can substitute it into the equation for RQS, 2x+4.

2(19.5)+4

39+4

43

Hope this helped!