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° 72° 36° 54°

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