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

Answer:

$(a)$

$x = 18.5$

$y = 22.5$

$(b)$

$x = 10$

Step-by-step 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

$y = \frac{1}{5} (7x - 17)$

Substitute $x = 18.5$

$y = \frac{1}{5} (7*18.5 - 17)$

$y = \frac{1}{5} (112.5)$

$y = 22.5$

Solving (b):

The triangle is right-angled.

So:

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

Collect Like Terms

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

$7x = 70$

$x = 10$