For which values of x and w is line a parallel to line d? Image shows that line a and line d are parallel. There is an intersecting line that creates three angles: (45x-5)°;(16x+2)°;(26^w)°. Choose one answer choice.

Answer 1

Since line a and line d are parallel, the corresponding angles will be equal. Therefore, we have:

45x - 5 = 16x + 2

Simplifying this equation, we get:

29x = 7

Dividing both sides by 29, we find:

x = 7/29

Now, since lines a and d are parallel, the third angle must also be equal. Therefore, we have:

45x - 5 = 26^w

Substituting the value of x we found:

45(7/29) - 5 = 26^w

Multiplying both sides by 29 to get rid of the fraction:

45(7) - 5(29) = 26^w

315 - 145 = 26^w

170 = 26^w

To find the value of w, we need to take the logarithm base 26 of both sides:

log base 26 of 170 = w

So, the answer is w = log base 26 of 170.