Question

In the given figure ,if AB DE, BAC=35° and CDE=53º, then find angle dce ​

Answer 1

ang DEC = 35° ( Alternate int. angles since DE || AB )

In Δ DCE

ang DCE + ang DEC + ang CDE = 180°

( Angle sum property )

ang DCE + 35° + 53° = 180

ang DCE = 180 – 88

ang DCE = 92°

Answer 2

Given :

• ∠BAC = 35°
• ∠CDE = 53°

To Find :

• ∠DCE

Solution :

$\longmapsto\tt{\angle{BAC}=\angle{CED}(Alternate\:Angles)}$

$\longmapsto\tt{\angle{CED}=35\degree}$

In Δ CDE ,

$\longmapsto\tt{\angle{CDE}+\angle{CED}+\angle{DCE}=180\degree(A.S.P)}$

$\longmapsto\tt{53\degree+35\degree+\angle{DCE}=180\degree}$

$\longmapsto\tt{\angle{DCE}+88\degree=180\degree}$

$\longmapsto\tt{\angle{DCE}=180\degree-88\degree}$

$\longmapsto\tt\bold{\angle{DCE}=92\degree}$

_______________________

VERIFICATION :

$\longmapsto\tt{\angle{CDE}+\angle{CED}+\angle{DCE}=180\degree}$

$\longmapsto\tt{53\degree+35\degree+92\degree=180\degree}$

$\longmapsto\tt\bold{180\degree=180\degree}$

HENCE VERIFIED