Question

In the given figure, AD||AB, AD || BC. If angle BDC = 30° and x:y = 11:19, then find angle DCE​

Answer 1

Given

• AD||AB
• AD || BC
• BDC = 30°
• x:y = 11:19

To Find

angle DCE

Topic

Lines and Angles

Solution

‣ Since AB || DC then BD is the transversal.

$\sf{ \to Therefore \: \angle ABD= \angle CDB}$

$\sf{ \to \red{\angle ABD= 30°}}$

»Now Assume ∆ABD

»Apply angle sum property

$\sf{⟹\angle BAD+ \angle ABD+\angle ADB = 180 \degree}$

$\sf{⟹90°+30°+X°= 180°}$

$\sf{⟹120°+ X°= 180°}$

$\sf{⟹X°= 180°-120°}$

$\sf{⟹ \green{X°= 60 \degree}}$

$\sf{x°=\angle DBC= 60° \: \: \purple{ [alternate \: interior \: angles]}}$

»Now Assume ∆DCB

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

$\sf{\angle BDC+\ angle DBC= \angle DCE \: \: \: \orange{ [exterior \: angle \: property]}}$

$\sf{⟹30°+ 60°= \angle DCE}$

$\bold{⟹ \pink{90° = \angle DCE}}$

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Answer 2

Answer:

60° Answer :;;;;;;;&-+&+8