Question

in the given fig find the value of x​

Answer 1

$\large{\mathfrak{\underline{\underline{Answer:-}}}}$

X = 50°

${\mathfrak{\underline{\underline{Step-By-Step-Explanation:-}}}}$

${\bf{{\angle}DEB \: + \: {\angle}DBC \: + \: {\angle}CBF \: = \: 180^{\circ}}}$

[Angle Property of a straight line]

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Angle Property of a straight line - Angle on a Straight line is 180°.

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Put Values

⟹ X + 3 + X + 20 + X + 7 = 180°

⟹ 3x + 30 = 180°

⟹ 3x = 180 - 30

⟹ 3x = 150

⟹ X = 150/3

⟹ X = 50

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$\huge{\bigstar{\boxed{\boxed{X \: = \: 50^{\circ}}}}}$

Answer 2

Answer:

$\huge{\pink{\green{\sf{\therefore x=50\degree}}}}$

$\huge{\pink{\green{\sf{\therefore \angle EBD=53\degree}}}}$

$\huge{\pink{\green{\sf{\therefore \angle DBC=70\degree}}}}$

$\huge{\pink{\green{\sf{\therefore \angle CBF=57\degree}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

▪In the given question information given about relation between three angles of a straight.

▪We have two find the angles of this straight line.

$\underline \bold{Given : } \\ \bold{ebf \: is \: a \: straight \: line}\\ \implies \angle EBD= x + 3 \\ \implies \angle DBC= x + 20 \\ \implies \angle CBF= x + 7 \\ \\ \underline \bold{To \:Find: } \\ \implies \angle EBD = ? \\ \implies \angle DBC= ? \\ \implies \angle CBF =?$

▪According to given question :

$\implies \angle EBD + \angle BDC + \angle CBF = 180 \degree \: \: \: \underline\bold{(linear \: pair)} \\ \implies x + 3 + x + 20 + x + 7 = 180 \degree \\ \implies 3x + 30 = 180 \degree \\ \implies 3x = 180 - 30 \\ \implies x = \frac{150}{3} \\ \bold{\implies x = 50 \degree} \\ \\ \bold{ \implies\angle EBF= x + 3 = 50 + 3 = 53 \degree} \\ \bold{ \implies\angle DBC = x + 20 = 50+ 20 =70 \degree} \\ \bold{ \implies\angle CBF= x + 7 = 50 + 7= 57\degree}$

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