SSC CGL Exam > SSC CGL Questions > In ΔABC. ∠A + ∠B = 145° and...
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In ΔABC. ∠A + ∠B = 145° and ∠C + 2∠B = 180°. State which one of the following relations is true? (SSC Sub. Ins. 2013)
- a)CA = AB
- b)CA < AB
- c)BC < AB
- d)CA > AB
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In ΔABC. ∠A + ∠B = 145° and ∠C + 2∠B = 180&d...
∠A + ∠B = 145°
∠C + 180° – 145° = 35°
∠C + 2∠B = 180°
⇒ 2∠B = 180° – 35° = 145°
⇒ ∠B = 145/2 = 72.5 ° = ∠A
∠B > ∠C
∴ CA > AB
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In ΔABC. ∠A + ∠B = 145° and ∠C + 2∠B = 180&d...
Given Information:
- ∠A + ∠B = 145°
- ∠C + 2∠B = 180°
Explanation:
To find the relation between the sides of the triangle, let's use the angle sum property of a triangle. The sum of the three angles in a triangle is always 180°.
Angle Sum Property:
- ∠A + ∠B + ∠C = 180°
Substitute the given angles:
- (145°) + ∠C = 180°
- ∠C = 180° - 145°
- ∠C = 35°
Now, let's use the given information to find the relation between the sides of the triangle.
Relation Between Sides:
- From the angle sum property, we know that ∠A + ∠B + ∠C = 180°.
- Substituting the given angles, we get: 145° + ∠B + 35° = 180°.
- ∠B = 180° - 145° - 35° = 0°.
Since ∠B = 0°, this implies that side CA is opposite the angle with measure 0°, which means side CA is the longest side in the triangle.
Therefore, the correct relation is:
CA > AB
So, the correct answer is option 'D'.
- ∠A + ∠B = 145°
- ∠C + 2∠B = 180°
Explanation:
To find the relation between the sides of the triangle, let's use the angle sum property of a triangle. The sum of the three angles in a triangle is always 180°.
Angle Sum Property:
- ∠A + ∠B + ∠C = 180°
Substitute the given angles:
- (145°) + ∠C = 180°
- ∠C = 180° - 145°
- ∠C = 35°
Now, let's use the given information to find the relation between the sides of the triangle.
Relation Between Sides:
- From the angle sum property, we know that ∠A + ∠B + ∠C = 180°.
- Substituting the given angles, we get: 145° + ∠B + 35° = 180°.
- ∠B = 180° - 145° - 35° = 0°.
Since ∠B = 0°, this implies that side CA is opposite the angle with measure 0°, which means side CA is the longest side in the triangle.
Therefore, the correct relation is:
CA > AB
So, the correct answer is option 'D'.
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In ΔABC. ∠A + ∠B = 145° and ∠C + 2∠B = 180°. State which one of the following relations is true? (SSC Sub. Ins. 2013)a)CA = ABb)CA < ABc)BC < ABd)CA > ABCorrect answer is option 'D'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about In ΔABC. ∠A + ∠B = 145° and ∠C + 2∠B = 180°. State which one of the following relations is true? (SSC Sub. Ins. 2013)a)CA = ABb)CA < ABc)BC < ABd)CA > ABCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In ΔABC. ∠A + ∠B = 145° and ∠C + 2∠B = 180°. State which one of the following relations is true? (SSC Sub. Ins. 2013)a)CA = ABb)CA < ABc)BC < ABd)CA > ABCorrect answer is option 'D'. Can you explain this answer?.
In ΔABC. ∠A + ∠B = 145° and ∠C + 2∠B = 180°. State which one of the following relations is true? (SSC Sub. Ins. 2013)a)CA = ABb)CA < ABc)BC < ABd)CA > ABCorrect answer is option 'D'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about In ΔABC. ∠A + ∠B = 145° and ∠C + 2∠B = 180°. State which one of the following relations is true? (SSC Sub. Ins. 2013)a)CA = ABb)CA < ABc)BC < ABd)CA > ABCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In ΔABC. ∠A + ∠B = 145° and ∠C + 2∠B = 180°. State which one of the following relations is true? (SSC Sub. Ins. 2013)a)CA = ABb)CA < ABc)BC < ABd)CA > ABCorrect answer is option 'D'. Can you explain this answer?.
Solutions for In ΔABC. ∠A + ∠B = 145° and ∠C + 2∠B = 180°. State which one of the following relations is true? (SSC Sub. Ins. 2013)a)CA = ABb)CA < ABc)BC < ABd)CA > ABCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC CGL.
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