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ABC and BDC are two triangles as shown in the given figure. If BDC is an isosceles triangle in which BD = DC. Find the value of ∠BDC.
- a)25o
- b)50o
- c)65o
- d)130o
- e)140o
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
ABC and BDC are two triangles as shown in the given figure. If BDC is ...
Since BD = CD,AngleDBC = AngleDCB (Let them be x)
Now three sides of triangles sums up to 180.AngleABC + AngleCBA + AngleCAB = 18040 +40+50+x+x = 180solving this, x = 25.
in triangle DBC,25+25+AngleDBC = 180angleDBC = 130
Now three sides of triangles sums up to 180.AngleABC + AngleCBA + AngleCAB = 18040 +40+50+x+x = 180solving this, x = 25.
in triangle DBC,25+25+AngleDBC = 180angleDBC = 130
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ABC and BDC are two triangles as shown in the given figure. If BDC is ...
Given:-ABC and BDC are two triangles
Now BDC is isoceles triangle
BD=DC
To find:- Angle BDC =?
Solution:- Since BD=DC
Using Isoceles triangle property,
Angle DBC = Angle DCB = Angle 'x'
[We are naming it as X for our. convenience]
Now, In triangle ABC,
Angle A + Angle B + Angle C = 180 degree
[Using angle sum property of triangle]
=> 40degree + (40+x)degree + (50+x)degree =180 degree
=> 2x=180 degree-130 degree
=> 2x=50degree
=>x=25 degree
Again, In triangle BDC,
Using angle aum property of triangle,
Angle BDC + Angle DBC + Angle DCB =180 degree
Angle BDC + 25 degree + 25 degree =180 degree
Angle BDC= 180 degree - 50degree
Angle BDC = 130 degree
Hence, Correct answer is option D
Now BDC is isoceles triangle
BD=DC
To find:- Angle BDC =?
Solution:- Since BD=DC
Using Isoceles triangle property,
Angle DBC = Angle DCB = Angle 'x'
[We are naming it as X for our. convenience]
Now, In triangle ABC,
Angle A + Angle B + Angle C = 180 degree
[Using angle sum property of triangle]
=> 40degree + (40+x)degree + (50+x)degree =180 degree
=> 2x=180 degree-130 degree
=> 2x=50degree
=>x=25 degree
Again, In triangle BDC,
Using angle aum property of triangle,
Angle BDC + Angle DBC + Angle DCB =180 degree
Angle BDC + 25 degree + 25 degree =180 degree
Angle BDC= 180 degree - 50degree
Angle BDC = 130 degree
Hence, Correct answer is option D
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