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In the adjoining figure is a square a line segment CX cuts AB at X and the diagonal BD at O such that angle COD is 80 degree and angle OXA is x degree find the value of x?
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In the adjoining figure is a square a line segment CX cuts AB at X and...
Solution:
Given, square ABCD, CX cuts AB at X and diagonal BD at O such that angle COD is 80 degree and angle OXA is x degree.
We need to find the value of x.
Let us first draw the figure.
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Angle OCB:
In triangle OCB,
∠OCB + ∠OBC + ∠O = 180° (Sum of angles of triangle)
∠OCB + 45° + 90° = 180° (As OC and OB are diagonals of square)
∠OCB = 45°
Angle OBC:
In triangle OBC,
∠OBC + ∠OBA + ∠A = 180° (Sum of angles of triangle)
∠OBC + 45° + 90° = 180° (As OA and OB are diagonals of square)
∠OBC = 45°
Angle BOC:
In triangle BOC,
∠BOC + ∠OBC + ∠OBC = 180° (Sum of angles of triangle)
∠BOC + 45° + 45° = 180°
∠BOC = 90°
So, triangle BOA is a right angled triangle with ∠BOA = 90°.
Angle COD:
Given, ∠COD = 80°
∠BOC = 90° (From above)
∠BOA = 90° (From above)
Therefore, ∠AOD = ∠BOC + ∠BOA = 90° + 90° = 180°.
∠COD + ∠AOD = 180° (Linear pair)
80° + ∠AOD = 180°
∠AOD = 100°
Angle OXA:
In triangle OXA,
∠OXA + ∠OAX + ∠X = 180° (Sum of angles of triangle)
∠OXA + 90° + 45° = 180° (As OA and CX are perpendicular)
∠OXA = 45°
Therefore, the value of x is 45°.
Given, square ABCD, CX cuts AB at X and diagonal BD at O such that angle COD is 80 degree and angle OXA is x degree.
We need to find the value of x.
Let us first draw the figure.
Angle OCB:
In triangle OCB,
∠OCB + ∠OBC + ∠O = 180° (Sum of angles of triangle)
∠OCB + 45° + 90° = 180° (As OC and OB are diagonals of square)
∠OCB = 45°
Angle OBC:
In triangle OBC,
∠OBC + ∠OBA + ∠A = 180° (Sum of angles of triangle)
∠OBC + 45° + 90° = 180° (As OA and OB are diagonals of square)
∠OBC = 45°
Angle BOC:
In triangle BOC,
∠BOC + ∠OBC + ∠OBC = 180° (Sum of angles of triangle)
∠BOC + 45° + 45° = 180°
∠BOC = 90°
So, triangle BOA is a right angled triangle with ∠BOA = 90°.
Angle COD:
Given, ∠COD = 80°
∠BOC = 90° (From above)
∠BOA = 90° (From above)
Therefore, ∠AOD = ∠BOC + ∠BOA = 90° + 90° = 180°.
∠COD + ∠AOD = 180° (Linear pair)
80° + ∠AOD = 180°
∠AOD = 100°
Angle OXA:
In triangle OXA,
∠OXA + ∠OAX + ∠X = 180° (Sum of angles of triangle)
∠OXA + 90° + 45° = 180° (As OA and CX are perpendicular)
∠OXA = 45°
Therefore, the value of x is 45°.
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In the adjoining figure is a square a line segment CX cuts AB at X and...
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In the adjoining figure is a square a line segment CX cuts AB at X and the diagonal BD at O such that angle COD is 80 degree and angle OXA is x degree find the value of x?
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In the adjoining figure is a square a line segment CX cuts AB at X and the diagonal BD at O such that angle COD is 80 degree and angle OXA is x degree find the value of x? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In the adjoining figure is a square a line segment CX cuts AB at X and the diagonal BD at O such that angle COD is 80 degree and angle OXA is x degree find the value of x? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the adjoining figure is a square a line segment CX cuts AB at X and the diagonal BD at O such that angle COD is 80 degree and angle OXA is x degree find the value of x?.
In the adjoining figure is a square a line segment CX cuts AB at X and the diagonal BD at O such that angle COD is 80 degree and angle OXA is x degree find the value of x? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In the adjoining figure is a square a line segment CX cuts AB at X and the diagonal BD at O such that angle COD is 80 degree and angle OXA is x degree find the value of x? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the adjoining figure is a square a line segment CX cuts AB at X and the diagonal BD at O such that angle COD is 80 degree and angle OXA is x degree find the value of x?.
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