VP
Joined: 28 Jul 2016
Posts: 1197
Given Kudos: 67
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE:Project Management (Investment Banking)
Re: Is triangle ABC a right triangle? 1. Angle BAC + angle ACB = 100
[#permalink]
28 Aug 2020, 03:18
(C) A right triangle is a triangle that has a 90° angle. Denote each angle by its vertex: angle BAC is angle A, angle ACB is angle C, and angle ABC is angle B.
Statement (1) is angle A + angle C = 100°. The sum of angles in any triangle is 180°. So, angle B + (angle A + angle C) = 180°. angle B + 100° = 180° angle B = 180° — 100° = 80°
So, you know one of the angles in the triangle. However, the two other angles are NOT defined. Angle A can be 90° when angle C is 10°. In this case, the triangle is a right triangle. Alternatively, angle A can be 60° when angle C is 40°. In this case, the triangle is NOT a right triangle. Therefore, statement (1) by itself is NOT sufficient.
Statement (2) is angle A + angle B = 120°. The sum of angles in any triangle is 180°. So, (angle A + angle B) + angle C = 180°. 120° + angle C = 180° angle C = 180° — 120° = 60°
So, you know one of the angles in the triangle. However, the other two angles are NOT defined. Angle A can be 90° when angle B is 30°. In this case, the triangle is a right triangle. Alternatively, angle A can be 60° when angle B is 60°. In this case, the triangle is NOT a right triangle. Therefore, statement (2) by itself is NOT sufficient.
When you use both statements together, the first one yields angle B = 80°, the second one yields angle C = 60°. So, you can calculate angle A = 180° — 80° — 60° = 40°. Therefore, both statements together define all the