Math, asked by girlofheaven, 7 months ago

please give answer fast​

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Answered by zaffarhkd0gmailcom
1

Answer:

angle A = 30 degree

angle B = 125degree

angle c= 25 degree

Answered by XxxRAJxxX
4

 \boxed{\huge{\bold{\red{\mathfrak{Question:}}}}}

 \red{\textsf{In a ΔABC, $ \angle A + \angle B = 125\degree$ and $ \angle B + \angle C = 150\degree $.}}

 \red{\textsf{ Find all the angle of ΔABC.}}

 \boxed{\huge{\bold{\red{\mathfrak{Solution:}}}}}

 \boxed{\blue{\mathsf{\because \angle A +  \angle B = 125\degree}}}

 \blue{\mathsf{\therefore \angle B = 125\degree - \angle A \: ......(i)}}

 \large{\green{\mathrm{Also,}}}

 \boxed{\blue{\mathsf{ \angle B + \angle C = 150\degree \: .......(ii)}}}

 \green{\textsf{Putting value of $ eq^n $ (i) in $ eq^n $ (ii), We get,}}

 \blue{\mathsf{\therefore 125\degree - \angle A +  \angle C = 150\degree}}

 \blue{\mathsf{\implies \angle C - \angle A = 150\degree - 125\degree}}

 \sf \blue{\implies \angle C - \angle A = 25\degree}

 \sf \blue{\implies \angle C = \angle A + 25\degree .......(iii)}

 {\green{\textsf{As we know that,}}}

 \large{\boxed{\green{\textsf{Sum of all angles of a Δ = 180°}}}}

 \large{\red{\textrm{Therefore,}}}

 \therefore \rm \blue{\angle A + \angle B + \angle C = 180\degree}

 \green{\textsf{From $ eq^n $ (i) and $ eq^n $ (iii), We get,}}

 \rm \blue{\therefore \angle A + 125\degree - \angle A + \angle A + 25\degree = 180\degree}

 \rm \blue{\implies \angle A + 125\degree \cancel{- \angle A}  \cancel{+ \angle A} + 25\degree = 180\degree}

  \rm \blue{\implies \angle A + 150\degree = 180\degree}

 \rm \blue{\implies angle A = 180\degree - 150\degree}

 \implies \rm \bf \boxed{ \blue{\angle A = 30\degree}}

 \large{\green{\textrm{Now,}}}

 \because \rm \red{\angle B = 125\degree - \angle A}

 \green{\textsf{Hence, $ \angle A = 30\degree $}}

 \therefore \rm \blue{\angle B = 125\degree - 30\degree}

 \implies \rm \bf \boxed{\blue{\angle B =  95\degree}}

 \large{\green{\textrm{Also,}}}

 \because \rm \red{\angle C = \angle A  + 25\degree}

 \green{\textsf{Hence, $ \angle A = 30\degree $}}

 \therefore \rm \blue{\angle C = 30\degree + 25\degree}

 \implies \rm \bf \boxed{\blue{\angle C = 55\degree}}

 \bold{\green{\textsf{Hence, all angles of ΔABC are}}}

 \bold{\green{\mathsf{30\degree, \: 95\degree \: and \: 55\degree}}}

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