Math, asked by hello121256, 2 months ago

in figure , ∆ABC=~∆ADC if angle BAC=30° and angle ABC=100°. find measure of angle ACD​

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Answered by Anonymous
33

Given :-

  • ∆ ABC ≅ ∆ ADC
  • ∠ BAC = 30°
  • ∠ ABC = 100°

To Find :-

  • ∠ ACD

Solution :-

In ∆ ABC,

  • ∠BAC = 30°
  • ∠ ABC = 100°

Now, we will find the value of ∠ACB,

Therefore,

=> ∠BAC + ∠ABC + ∠ACB = 180°

( Angle sum property of a Triangle)

Now, we will put the given values,

=> 30° + 100° + ∠ACB = 180°

=> 130° + ∠ACB = 180°

=> ∠ACB = 180° - 130°

=> ∠ACB = 50°

Therefore, ∠ACB = 50°

Now, since ∆ ABC ≅ ∆ ADC, therefore,

  • ∠ ACB = ∠ ACD ( Corresponding parts of congruent triangles)

Therefore,

∠ ACB = ∠ ADC = 50°

Hope that helps!

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