Question

find the value of x


plzzz answer this question ​

Answer 1

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$\color{red}\huge{\underline{\underline{\mathfrak{Question:-}}}}$

A diagram given of a triangle with its outer angles as 110° and 100° . And 1 interior angle is given as x°.

We have to find the value of x.

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$\color{blue}\huge{\underline{\underline{\mathfrak{Answer}}}}$

${\blue{\bold{\text{x = 30 degree }}}}$

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$\color{orange}\huge{\underline{\underline{\mathfrak{Solution:-}}}}$

${\blue{\bold{\text{Given}}}}$

• A triangle ABC
• Exterior angle ACE and angle ABD are of 110° and 100° respectively.

${\blue{\bold{\text{To find=x}}}}$

${\blue{\bold{\text{We know that}}}}$

Angle ABD+ angle ABC =180° [Linear pair angles].....(1)

Similarly angle ACE+angle ACB is also 180°..........(2)

From eqn (1) and (2) we get angle ACB=70° and angle ABC=80°

${\blue{\bold{\text{In triangleABC}}}}$

Sum of all interior angles is 180° by interior angle sum property .

So,

70°+80°+x°=180°

150°+x°=180°

x°=180°-150°

x°=30°

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Hope it helps

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• $\sf \angle ABD = 100°$

• $\sf \angle ACE = 110°$

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

• Measure of angle 'x'

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Here,

$\:\:$

$\sf \longmapsto \angle ABD + \angle ABC = 180°$ [ Linear pair ]

$\:\:$

$\sf \longmapsto 100° + \angle ABC = 180°$

$\:\:$

$\sf \longmapsto \angle ABC = 180 - 100$

$\:\:$

$\purple\dashrightarrow$ $\bf\angle ABC = 80°$

$\:\:$

$\sf \longmapsto \angle ACB + \angle ACE = 180°$ [ Linear pair ]

$\:\:$

$\sf \longmapsto \angle ACB + 110° = 180°$

$\:\:$

$\sf \longmapsto \angle ACB = 180 - 110$

$\:\:$

$\purple\dashrightarrow$ $\bf\angle ACB = 70°$

$\:\:$

$\underline{\bold{\texttt{We know that,}}}$

$\:\:$

$\purple\longrightarrow$ $\sf x + \angle ABC + \angle ACB = 180°$

[ Sum of all angle of a triangle is 180° ]

$\:\:$

$\sf \longmapsto x + 80° + 70° = 180°$

$\:\:$

$\sf \longmapsto x = 180 - 150$

$\:\:$

$\red\longrightarrow$ $\boxed {x = 30°}$

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