Question

Determine the value of x for which r // s if m∠1 = 60, and m∠2=70-4x

Answer 1

So, the value of x for which line r is parallel to line s is x = 5/2.

Explanation:

Given:

m∠1 = 60

m∠2 = 70 - 4x

If r is parallel to s, then m∠1 must be congruent to the corresponding angle on line s. In other words, m∠1 = m∠3, where ∠3 is the corresponding angle on line s.

So, we have:

m∠1 = m∠3

60 = m∠3

Now, we need to find the value of ∠2 in terms of x and set it equal to 60:

m∠2 = 70 - 4x

So,

70 - 4x = 60

Now, you can solve for x:

70 - 4x = 60

Subtract 70 from both sides:

-4x = 60 - 70

-4x = -10

Now, divide by -4:

x = (-10) / (-4)

x = 10 / 4

x = 5/2

So, the value of x for which line r is parallel to line s is x = 5/2.