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