Discussion
In ΔABC, the side AB is produced to E and side CA is produced to D. If ∠BAD = 125° and ∠EBC = 100°, then which of the following is true ?
Answer: C
The true statement is the difference between ∠ABC and ∠ACB is 35°.
∠BAD is the exterior angle at A (CA produced to D), so ∠BAC = 180° − 125° = 55°. ∠EBC is the exterior angle at B (AB produced to E), so ∠ABC = 180° − 100° = 80°. The angle sum then gives ∠ACB = 180° − 55° − 80° = 45°.
So ∠ABC − ∠ACB = 80° − 45° = 35°.
The others are false. The angles 55°, 80° and 45° are all different, so the triangle is not isosceles. AB is opposite the smallest angle (45° at C) and BC is opposite 55°, so AB is shorter than BC, not longer. ∠BAC − ∠ACB is 10°, not 20°.
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