The side BC of a triangle ABC is extended to a point D. If ∠ ACD = 117º and ∠ ABC = 5/8 ∠ BAC, then what is the measure of ∠ ABC?

The side BC of a triangle ABC is extended to a point D. If…

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

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 45º

∠ABC = 5y and ∠BAC = 8y (∠ABC = 5/8 of ∠BAC)

Now,

⇒ 5y + 8y = 117° (the exterior angle is equal to sum of interior opposite angles)

⇒ 13y = 117°

⇒ x = 9

Hence,

∠ABC = 5x = 45°

SSC CHSL 2021 PYQ — Question 55