Question

In the given figure, angle DBC= 56° , angle DCE= 96°, find the value of x
please teach me step by step​

Answer 1

$\huge{Solution:-}$

☞ Answer:

→ x = 40°

☞ Step-by-step explanation :

→ Given ∠DCE = 96°, ∠DBC = 56° and ∠BAC is taken as x.

Now,

∠DCE + ∠DCB = 180° (Linear pairs are supplementary)

⇒96° + ∠DCB = 180°

⇒ ∠DCB = 180° - 96°

⇒ ∠DCB = 84°

In ∆BCD,

∠DBC + ∠DCB + ∠BDC = 180°

[Angle sum property of a triangle]

⇒56° + 84° + ∠BDC = 180°

⇒140° + ∠BDC = 180°

⇒ ∠BDC = 180° - 140°

⇒ ∠BDC = 40°

Now,

We see that ABCD is a cyclic quadrilateral.

Therefore,

∠BDC = 40° = x

[Angles in the same segment of a circle are equal]

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Hope this helps!❤