Question

100 points!!

The value of X is 12 degrees less than the value of y. Find the values of both X and y

Answer 1

`x = (y - 12) \\ then \\ x + y = 180 \\ (y - 12) + y = 180 \\ y - 12 + y = 180 \\ y + y = 180 + 12 \\ 2y = 192 \\ y = (192)/(2 ) \\`

y = 96°

so now, substituting the value of y,

x = ( y - 12 )

x = ( 96 - 12 )

x = 84°

so value of

x = 84°

y = 96°

Answer 2

x = 84

y = 96

Explanation:

Alternate interior angles are a pair of nonadjacent interior angles that are on opposite sides of the transversal. Alternate interior angles are equal.

Therefore, x = y - 12

Angles on a straight line add up to 180°

Therefore, x + y = 180

Substituting x = y - 12 into x + y = 180 and solve for y:

⇒ y - 12 + y = 180

⇒ 2y - 12 = 180

⇒ 2y = 192

⇒ y = 96

Substitute found value for y into x = y - 12 and solve for x:

⇒ x = 96 - 12

⇒ x = 84