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In the quadrilateral given above, AB = AD =10, BC = CD = 5. Which of
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10 Jan 2025, 01:58
10 Jan 2025, 01:58
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In the quadrilateral given above, AB = AD =10, BC = CD = 5. Which of the following can be the value of the angle BAD?
A. 45
B. 60
C. 75
D. 90
E. 122.5
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Re: In the quadrilateral given above, AB = AD =10, BC = CD = 5. Which of
[#permalink]
10 Jan 2025, 05:14
10 Jan 2025, 05:14
pls explain
Re: In the quadrilateral given above, AB = AD =10, BC = CD = 5. Which of
[#permalink]
10 Jan 2025, 07:20
10 Jan 2025, 07:20
1
Expert Reply
As $\(\mathrm{AB}=\mathrm{AD}=10 \& \mathrm{BC}=\mathrm{CD}=5\)$, so the opposite angles must also be equal.
If angle BAD is 60 degrees, the triangle ABD becomes equilateral and side BD comes 10 , which in triangle $\(B C D\)$ gives $\(B C+C D=5+5=10=B D\)$, which is not possible as the sum of the sides in a triangle is always greater than the third side.
To satisfy $\(\mathrm{BC}+\mathrm{CD}>\mathrm{BD}\)$, the length of BD must be less than 10 which implies the measure of angle opposite to side BD in triangle ABD must be less than 60 .
Hence only option (A) i.e. 45 degrees can be the measure of angle BAD, so is correct.
If angle BAD is 60 degrees, the triangle ABD becomes equilateral and side BD comes 10 , which in triangle $\(B C D\)$ gives $\(B C+C D=5+5=10=B D\)$, which is not possible as the sum of the sides in a triangle is always greater than the third side.
To satisfy $\(\mathrm{BC}+\mathrm{CD}>\mathrm{BD}\)$, the length of BD must be less than 10 which implies the measure of angle opposite to side BD in triangle ABD must be less than 60 .
Hence only option (A) i.e. 45 degrees can be the measure of angle BAD, so is correct.
