Question

In ABCD, ∠B = 117° and ∠C = 19°. Which statement about the sides of ABCD must be true?

a) AB < BC
b) AB > BC
c) AB = BC
d) Not enough information to determine.

Answer 1

The side opposite the larger angle in a triangle is the longer side, so given angles ∠B and ∠C in triangle ABCD, with ∠B being considerably larger, it must be true that side AB is greater than side BC.

Step-by-step explanation:

When considering the sides of a triangle in relation to its angles, angle size can give insight into the relative lengths of the sides opposite those angles. In the case of triangle ABCD, we know two angles: ∠B = 117° and ∠C = 19°. According to the Triangle Inequality Theorem, the larger the angle in a triangle, the longer the side opposite it.

Given that ∠B is much larger than ∠C, we can deduce that AB > BC because the side opposite the larger angle is always longer in a triangle. Hence, the correct answer to the question is (b) AB > BC.