Question

Select all the choices that apply to △ABC with: ∠B=110°, ∠A=∠C, AC=50. Options:

A) Obtuse
B) Acute
C) Scalene
D) Isosceles
E) ASA
F) AAS
G) SSA
H) SAS

Answer 1

△ABC is an obtuse and isosceles triangle, with ∠B measuring 110° and equal angles ∠A and ∠C. We cannot determine triangle congruence rules such as ASA, AAS, SSA, or SAS based on the given information.

Step-by-step explanation:

To determine the characteristics of △ABC with ∠B=110°, ∠A=∠C, and AC=50, we first note that ∠B is greater than 90°, making △ABC an obtuse triangle since it has one angle that is greater than 90°. Secondly, since ∠A and ∠C are equal and the sum of all angles in a triangle is 180°, we can find ∠A and ∠C each by calculating (180° - ∠B) / 2 which gives us 35° for both angles, confirming that △ABC is also isosceles. As for the triangle congruence or similarity rules, we don't have enough information on the other side lengths to determine congruency through ASA, AAS, SSA, or SAS as we have been given only one side length (AC=50).