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If a perpendicular drawn from an obtuse-angled vertex of a rhombus to the opposite side bisect the side , all angles of the rhombus are a) 70⁰,110⁰,70⁰,110⁰ b) 40⁰,140⁰,40⁰,140⁰ c) 50⁰,130⁰,50⁰,130⁰ d) 60⁰,120⁰,60⁰,120⁰?
Verified Answer
If a perpendicular drawn from an obtuse-angled vertex of a rhombus to ...
The correct answer is d) 60degree,120degree,60degree,120degree.
In a rhombus, all angles are equal, so if a perpendicular drawn from an obtuse-angled vertex of a rhombus to the opposite side bisects the side, the angles at the vertex must be half of the total angle measure of the rhombus. Since the total angle measure of a rhombus is 360
degree, each angle must be 360
degree/2 = 180
degree/2 = 90
degree.
In addition, the perpendicular bisects the side, so each angle at the vertex is 90
degree/2 = 45
degree. Hence, the angles of the rhombus are 60
degree, 120
degree, 60
degree, and 120
degree.
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Most Upvoted Answer
If a perpendicular drawn from an obtuse-angled vertex of a rhombus to ...
To solve this problem, let's consider the given conditions and use the properties of a rhombus.
Conditions:
1. The rhombus has an obtuse-angled vertex.
2. A perpendicular is drawn from this vertex to the opposite side, which bisects the side.
Let's analyze each option and see if it satisfies these conditions.
a) 70⁰, 110⁰, 70⁰, 110⁰
b) 40⁰, 140⁰, 40⁰, 140⁰
c) 50⁰, 130⁰, 50⁰, 130⁰
d) 60⁰, 120⁰, 60⁰, 120⁰
We know that the opposite angles of a rhombus are equal. So, let's consider the angles of the rhombus.
Since the perpendicular bisects the side, the opposite sides of the rhombus are divided into two equal parts. Let's label the rhombus as ABCD, with AB as the side bisected by the perpendicular.
Let's assume that the obtuse angle is ∠A. Since the perpendicular bisects AB, it creates two equal segments. Let's label the point where the perpendicular meets AB as E. So, AE = EB.
Now, let's consider the angles of the rhombus:
∠A = Obtuse angle (unknown)
∠B = 180⁰ - ∠A (opposite angles are supplementary)
∠C = ∠A (opposite angles are equal)
∠D = 180⁰ - ∠C = 180⁰ - ∠A (opposite angles are supplementary)
From the given options, it can be observed that option a) satisfies the conditions.
∠A = 70⁰
∠B = 180⁰ - 70⁰ = 110⁰
∠C = 70⁰
∠D = 180⁰ - 70⁰ = 110⁰
Therefore, the correct answer is option a) 70⁰, 110⁰, 70⁰, 110⁰.
Conditions:
1. The rhombus has an obtuse-angled vertex.
2. A perpendicular is drawn from this vertex to the opposite side, which bisects the side.
Let's analyze each option and see if it satisfies these conditions.
a) 70⁰, 110⁰, 70⁰, 110⁰
b) 40⁰, 140⁰, 40⁰, 140⁰
c) 50⁰, 130⁰, 50⁰, 130⁰
d) 60⁰, 120⁰, 60⁰, 120⁰
We know that the opposite angles of a rhombus are equal. So, let's consider the angles of the rhombus.
Since the perpendicular bisects the side, the opposite sides of the rhombus are divided into two equal parts. Let's label the rhombus as ABCD, with AB as the side bisected by the perpendicular.
Let's assume that the obtuse angle is ∠A. Since the perpendicular bisects AB, it creates two equal segments. Let's label the point where the perpendicular meets AB as E. So, AE = EB.
Now, let's consider the angles of the rhombus:
∠A = Obtuse angle (unknown)
∠B = 180⁰ - ∠A (opposite angles are supplementary)
∠C = ∠A (opposite angles are equal)
∠D = 180⁰ - ∠C = 180⁰ - ∠A (opposite angles are supplementary)
From the given options, it can be observed that option a) satisfies the conditions.
∠A = 70⁰
∠B = 180⁰ - 70⁰ = 110⁰
∠C = 70⁰
∠D = 180⁰ - 70⁰ = 110⁰
Therefore, the correct answer is option a) 70⁰, 110⁰, 70⁰, 110⁰.
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If a perpendicular drawn from an obtuse-angled vertex of a rhombus to the opposite side bisect the side , all angles of the rhombus are a) 70⁰,110⁰,70⁰,110⁰ b) 40⁰,140⁰,40⁰,140⁰ c) 50⁰,130⁰,50⁰,130⁰ d) 60⁰,120⁰,60⁰,120⁰?
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If a perpendicular drawn from an obtuse-angled vertex of a rhombus to the opposite side bisect the side , all angles of the rhombus are a) 70⁰,110⁰,70⁰,110⁰ b) 40⁰,140⁰,40⁰,140⁰ c) 50⁰,130⁰,50⁰,130⁰ d) 60⁰,120⁰,60⁰,120⁰? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about If a perpendicular drawn from an obtuse-angled vertex of a rhombus to the opposite side bisect the side , all angles of the rhombus are a) 70⁰,110⁰,70⁰,110⁰ b) 40⁰,140⁰,40⁰,140⁰ c) 50⁰,130⁰,50⁰,130⁰ d) 60⁰,120⁰,60⁰,120⁰? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a perpendicular drawn from an obtuse-angled vertex of a rhombus to the opposite side bisect the side , all angles of the rhombus are a) 70⁰,110⁰,70⁰,110⁰ b) 40⁰,140⁰,40⁰,140⁰ c) 50⁰,130⁰,50⁰,130⁰ d) 60⁰,120⁰,60⁰,120⁰?.
If a perpendicular drawn from an obtuse-angled vertex of a rhombus to the opposite side bisect the side , all angles of the rhombus are a) 70⁰,110⁰,70⁰,110⁰ b) 40⁰,140⁰,40⁰,140⁰ c) 50⁰,130⁰,50⁰,130⁰ d) 60⁰,120⁰,60⁰,120⁰? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about If a perpendicular drawn from an obtuse-angled vertex of a rhombus to the opposite side bisect the side , all angles of the rhombus are a) 70⁰,110⁰,70⁰,110⁰ b) 40⁰,140⁰,40⁰,140⁰ c) 50⁰,130⁰,50⁰,130⁰ d) 60⁰,120⁰,60⁰,120⁰? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a perpendicular drawn from an obtuse-angled vertex of a rhombus to the opposite side bisect the side , all angles of the rhombus are a) 70⁰,110⁰,70⁰,110⁰ b) 40⁰,140⁰,40⁰,140⁰ c) 50⁰,130⁰,50⁰,130⁰ d) 60⁰,120⁰,60⁰,120⁰?.
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