Question

solve for each variable i don’t need work shown just the answers please thank you very much i have 2 hours to get this done

Answer 1

`(a)`

`x = 18.5`

`y = 22.5`

`(b)`

`x = 10`

Explanation:

Solving (a):

7x - 19 and 3x + 14 are interior angles.

So:

`7x - 19 + 3x +14 = 180`

Collect like terms

`7x + 3x = 180 - 14 + 19`

`10x = 185`

`x = 18.5`

7x - 19 and 5y - 2 are equal angles --- corresponding angles

So:

`5y - 2 = 7x - 19`

Make 5y the subject

`5y = 7x - 19+2`

5y = 7x -17

Make y the subject

`y = (1)/(5) (7x - 17)`

Substitute
`x = 18.5`

`y = (1)/(5) (7*18.5 - 17)`

`y = (1)/(5) (112.5)`

`y = 22.5`

Solving (b):

The triangle is right-angled.

So:

`5x + 3 + 2x + 17 + 90 = 180`

Collect Like Terms

`5x + 2x = 180 - 90 - 17-3`

`7x = 70`

`x = 10`