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07 Jul 2020, 07:17
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Difficulty:
35%
(medium)
Question Stats:
66% (01:39) correct
34%
(01:34)
wrong
based on 171
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Is triangle ABC a right triangle?
1) ∠BAC + ∠ACB = 100
2) ∠BAC + ∠ABC = 120
1) ∠BAC + ∠ACB = 100
2) ∠BAC + ∠ABC = 120
yashikaaggarwal
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07 Jul 2020, 10:04
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1) ∠BAC + ∠ACB = 100
No information about 3rd angle (insufficient)
2) ∠BAC + ∠ABC = 120
No information about 3rd angle (insufficient)
Statement 1&2: add both equations
∠BAC + ∠ACB = 100 ----------(1)
∠BAC + ∠ABC = 120 ----------(2)
=> 2∠BAC + ∠ACB + ∠ABC = 220 ---------(3)
Also, interior angles of triangle ∠BAC + ∠ACB + ∠ABC = 180 -------------(4)
Equating 3&4 equation.
2∠BAC + ∠ACB + ∠ABC = 220
∠BAC + ∠ACB + ∠ABC = 180
∠BAC = 40
∠ACB = 60
∠ABC = 80
None of the three angles is 90°
Hence ABC is not a right angle triangle.
(Sufficient)
Answer is C
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No information about 3rd angle (insufficient)
2) ∠BAC + ∠ABC = 120
No information about 3rd angle (insufficient)
Statement 1&2: add both equations
∠BAC + ∠ACB = 100 ----------(1)
∠BAC + ∠ABC = 120 ----------(2)
=> 2∠BAC + ∠ACB + ∠ABC = 220 ---------(3)
Also, interior angles of triangle ∠BAC + ∠ACB + ∠ABC = 180 -------------(4)
Equating 3&4 equation.
2∠BAC + ∠ACB + ∠ABC = 220
∠BAC + ∠ACB + ∠ABC = 180
∠BAC = 40
∠ACB = 60
∠ABC = 80
None of the three angles is 90°
Hence ABC is not a right angle triangle.
(Sufficient)
Answer is C
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globaldesi
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28 Aug 2020, 03:18
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(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
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
