Angles.

Geometry Level 1

In the figure above, ∠ A B E \angle ABE = ∠ E C D \angle ECD and ∠ E B D \angle EBD = ∠ A C E \angle ACE . If ∠ B A C = 8 0 ∘ \angle BAC = 80 ^ \circ and ∠ B E C = 10 0 ∘ \angle BEC = 100 ^ \circ then, what is the value of obtuse ∠ B D C \angle BDC .


The answer is 120.

Gaurav Singh by Gaurav singh , 21, India

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1 solution

Gaurav Singh
Mar 23, 2014

Given that ∠ A B E \angle ABE = ∠ E C D \angle ECD and ∠ A C E \angle ACE = ∠ E B D \angle EBD So, ∠ A B D \angle ABD also equal to ∠ A C D \angle ACD . and sum of all angles of a quad. is 360 degree using both find ∠ B D C \angle BDC .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

{Assume "/.." represents angle} 2 /..ACD + /.. DBC+ /.. DCB= 100 & /.. DCA + /.. DBC + /.. DCB = 80. From that /.. ACD=20 AND again /.. A + /.. ABD + /.. ACD + /.. BDC = 360 , so /.. BDC = 240 (As /.. ABD = /.. ACD). Obtuse angle /.. BDC =120. Remember obtuse angle means more than 90 and less than 180. Do not get confuse as I did to recognize the obtuse angle by seeing picture.

Swayam Bikash Ghosh - 7 years, 2 months ago

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