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Vera_Pavlovna [14]
3 years ago
10

Pls answer the question attached

Mathematics
1 answer:
barxatty [35]3 years ago
6 0

\huge\mathfrak{\underline{answer:}}

\large\bf{\angle ACD = 105°}

__________________________________________

\large\bf{\underline{Here:}}

  • BCD is an isosceles right triangle , right angled at D
  • ABC is an equilateral triangle

\large\bf{\underline{To\:find:}}

  • ∠ ACD

\large\bf{In\: triangle\:ABC:}

❒ Sum of all angles is 180° , since it is an equilateral triangle all the three angles would be same

\large\bf{\underline{So}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼\angle ACB = \frac{180}{3}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼\angle ACB = 60°}

\large\bf{In\: triangle\:BDC}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼\angle D = 90°}

\bf{⟼\angle DBC =\angle DCB }(Isosceles triangle)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼\angle DBC + \angle BDC + \angle DCB = 180° }

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼2\angle DCB + 90° = 180°}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼2\angle DCB = 180 -90}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼\angle DCB = \frac{90}{2}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟼\angle DCB = 45°}

\large\bf{\underline{Therefore,}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟹\angle ACD = \angle ACB + \angle DCB}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\bf{⟹\angle ACD = 60+45}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{⟹\angle ACD = 105°}

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