Letters a, b, c, and d are angle measures. Lines f and g are intersected by line n. At the intersection of lines n and g, clockwise from the top, the angles are: a, 75 degrees, blank, b. At the intersection of lines n and f, clockwise from the top, the angles are blank, blank, d, c. Which should equal 105° to prove that f ∥ g?
a.
b.
c.
d.

Respuesta :

Answer:

∠a = 105°

Step-by-step explanation:

If a set of 2 parallel lines, line f and line g, are intersected by another line n,  then at each of the parallel lines, then at each of the parallel lines adjacent angles are supplementary (i.e their sum is equal to 180° as shown in fig 1

Following this rule, comparing fig 2 with fig 1

                  [tex]\implies a = 180 -75\\\implies a =105[/tex]

If f and g are parallel then ∠a must be equal to ∠d

                   [tex]\implies \angle a = \angle d =105^{o}[/tex]

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Answer:

a

Step-by-step explanation: