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Is triangle ABC a right triangle? 1. Angle BAC + angle ACB = 100

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unraveled
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Is triangle ABC a right triangle? 1. Angle BAC + angle ACB = 100 [#permalink] New post   07 Jul 2020, 07:17
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Is triangle ABC a right triangle?

1) ∠BAC + ∠ACB = 100
2) ∠BAC + ∠ABC = 120
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C
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yashikaaggarwal
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Re: Is triangle ABC a right triangle? 1. Angle BAC + angle ACB = 100 [#permalink] New post   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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Re: Is triangle ABC a right triangle? 1. Angle BAC + angle ACB = 100 [#permalink] New post   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
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Re: Is triangle ABC a right triangle? 1. Angle BAC + angle ACB = 100 [#permalink] New post   29 Aug 2020, 05:46
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unraveled wrote:
Is triangle ABC a right triangle?

1) ∠BAC + ∠ACB = 100
2) ∠BAC + ∠ABC = 120


Statement 1 tells us that the third angle in the triangle is 80 degrees, because the three angles add to 180. But one of the two angles in the equation could be 90. Similarly Statement 2 tells us the unmentioned angle is 60 degrees, but one of the two angles in the equation could be 90. Using both Statements, we know we have an 80 and a 60 degree angle in the triangle, so the third angle must be 40 degrees, and the triangle is not a right triangle. So the answer is C.
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Re: Is triangle ABC a right triangle? 1. Angle BAC + angle ACB = 100 [#permalink] New post   23 Feb 2023, 12:02
unraveled wrote:
Is triangle ABC a right triangle?

1) ∠BAC + ∠ACB = 100
2) ∠BAC + ∠ABC = 120


None of the equation alone is sufficient

Together they are sufficient(Option C)

Angle ABC + Angle BCA +Angle CAB =180........(3)

(3)-(1),we get Angle ABC=80
(3)-(2),we get Angle ACB=60

Hence triangle ABC is not a right triangle
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Re: Is triangle ABC a right triangle? 1. Angle BAC + angle ACB = 100 [#permalink]
23 Feb 2023, 12:02
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