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ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. If ∠BDC = 50°, then ∠A is (SSC CGL 2nd Sit. 2013)
- a)100°
- b)90°
- c)120°
- d)60°
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
ABC is a triangle. The bisectors of the internal angle ∠B and exte...
From question ∠BDC = 50°
In ΔBDC, ∠DBC + ∠BDC + ∠BCD = 180°
∠B + ∠C = 40 × 2 = 80°
From ΔABC, ∠A + ∠B + ∠C = 180°
∠A + 80° = 180°
∠A = 180° – 80° = 100°
Most Upvoted Answer
ABC is a triangle. The bisectors of the internal angle ∠B and exte...
Let's call the bisectors of angle A, angle B, and angle C as AD, BE, and CF respectively.
Since AD is the bisector of angle A, it divides angle A into two equal angles. Let's call these angles BAD and CAD. Similarly, let's call the angles divided by BE as CBE and ABE, and the angles divided by CF as ACF and BCF.
Now, let's consider angle BAD. It is equal to angle CAD because AD is the bisector of angle A. Similarly, angle CBE is equal to angle ABE because BE is the bisector of angle B. Finally, angle ACF is equal to angle BCF because CF is the bisector of angle C.
Since angle BAD is equal to angle CAD, and angle CBE is equal to angle ABE, we can conclude that angle BAD + angle CBE = angle CAD + angle ABE.
Now, let's consider angle A + angle B + angle C. This is the sum of all the internal angles of triangle ABC. We know that angle BAD + angle CAD = angle A, and angle CBE + angle ABE = angle B. Therefore, angle A + angle B + angle C = (angle BAD + angle CAD) + (angle CBE + angle ABE) + angle C.
Using the previous conclusion, we can rewrite this as angle BAD + angle CBE + angle C = angle CAD + angle ABE + angle C.
Since angle ACF is equal to angle BCF, we can substitute angle C with angle ACF. Therefore, angle A + angle B + angle C = (angle BAD + angle CBE) + angle ACF.
We can see that angle BAD + angle CBE + angle ACF is equal to angle A + angle B + angle C.
Therefore, the sum of the angles BAD, CBE, and ACF is equal to the sum of the angles A, B, and C, which is 180 degrees.
Since AD is the bisector of angle A, it divides angle A into two equal angles. Let's call these angles BAD and CAD. Similarly, let's call the angles divided by BE as CBE and ABE, and the angles divided by CF as ACF and BCF.
Now, let's consider angle BAD. It is equal to angle CAD because AD is the bisector of angle A. Similarly, angle CBE is equal to angle ABE because BE is the bisector of angle B. Finally, angle ACF is equal to angle BCF because CF is the bisector of angle C.
Since angle BAD is equal to angle CAD, and angle CBE is equal to angle ABE, we can conclude that angle BAD + angle CBE = angle CAD + angle ABE.
Now, let's consider angle A + angle B + angle C. This is the sum of all the internal angles of triangle ABC. We know that angle BAD + angle CAD = angle A, and angle CBE + angle ABE = angle B. Therefore, angle A + angle B + angle C = (angle BAD + angle CAD) + (angle CBE + angle ABE) + angle C.
Using the previous conclusion, we can rewrite this as angle BAD + angle CBE + angle C = angle CAD + angle ABE + angle C.
Since angle ACF is equal to angle BCF, we can substitute angle C with angle ACF. Therefore, angle A + angle B + angle C = (angle BAD + angle CBE) + angle ACF.
We can see that angle BAD + angle CBE + angle ACF is equal to angle A + angle B + angle C.
Therefore, the sum of the angles BAD, CBE, and ACF is equal to the sum of the angles A, B, and C, which is 180 degrees.
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ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. If ∠BDC = 50°, then ∠A is (SSC CGL 2nd Sit. 2013)a)100°b)90°c)120°d)60°Correct answer is option 'A'. Can you explain this answer?
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ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. If ∠BDC = 50°, then ∠A is (SSC CGL 2nd Sit. 2013)a)100°b)90°c)120°d)60°Correct answer is option 'A'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. If ∠BDC = 50°, then ∠A is (SSC CGL 2nd Sit. 2013)a)100°b)90°c)120°d)60°Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. If ∠BDC = 50°, then ∠A is (SSC CGL 2nd Sit. 2013)a)100°b)90°c)120°d)60°Correct answer is option 'A'. Can you explain this answer?.
ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. If ∠BDC = 50°, then ∠A is (SSC CGL 2nd Sit. 2013)a)100°b)90°c)120°d)60°Correct answer is option 'A'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. If ∠BDC = 50°, then ∠A is (SSC CGL 2nd Sit. 2013)a)100°b)90°c)120°d)60°Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. If ∠BDC = 50°, then ∠A is (SSC CGL 2nd Sit. 2013)a)100°b)90°c)120°d)60°Correct answer is option 'A'. Can you explain this answer?.
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