The side BC of a triangle ABC is extended to a point D. If ∠ACD = 117° and ∠ABC = $\frac{5}{8}$ ∠BAC, then what is the measure of ∠ABC ?

45°

We are given that :-

∠ABC = $\frac{5}{8}$ ∠BAC

Let us consider that ∠ABC = 5A  and ∠BAC = 8A

By using property :- Sum of opposite interior angles is equal to exterior angle.

5A + 8A = 117º

13A = 117º

1A = 9º

Now, ∠ABC = 5A = 5 × 9º

= 45º