Question

AD paerpindicular to AB , AD parallel to BC if angle BDC = 32 degrees and x : y = 11:19 .find angle DCE​

Answer 1

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Answer 2

Step-by-step explanation:

Since AB || DC then BD is the transversal.

→ Therefore ∠ABD = ∠CDB

→ ∠ABD = 32°

>>Now Assume ΔABD

>>Apply angle sum property

∠BAD + ∠ABD + ∠ADB = 180*

90 +32 +X° = 180"

122" + X 180"

X° = 180° - 122°

⇒X° = 58°

x° = ∠DBC = 58° |alternate interior angles

>>Now Assume ΔDCB

>Important property- An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

∠BDC + ∠DBC = ∠DCE

=> 32° + 58° = ∠DCE

=> 90¹ = ∠DCE

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