Question

solve the question seen in the attachment

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Answer 1

Given :-

• AB = DC
• AC = DB
• ∠BAC = 60°
• ∠DBC = 45°

Solution :-

in ∆ABC and ∆DCB

• AB = DC (given)
• AC = DB (given)
• BC = BC (common)

hence,

Yes ∆ABC ≅ ∆DCB by SSS congruency rule

___________________________

• CPCT : corresponding parts of congruent triangles

(two or more triangles are congruent, then all of their corresponding angles and sides are equal.)

now, ∆ABC ≅ ∆DCB

➪ ∠ACB = ∠DBC (by CPCT)

$\bold{: \implies \boxed{ \bold{∠ACB = 45 \degree}}}$

and now, in ∆ABC

we know that,

• sum of all interior angles of the triangle is equal to 180°

$\bold{: \implies ∠ABC + ∠ACB + ∠BAC = 180°} \\ \\ \bold{: \implies∠ABC +45 \degree + 60 \degree = 180 \degree } \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies ∠ABC + 105 \degree = 180 \degree } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies ∠ABC = 180 \degree - 105 \degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \boxed{ \bold{∠ABC = 75 \degree}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hence,

• ∠ACB = 45°
• ∠ABC = 75 °

Answer 2

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