Question

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

Answer 1

★ 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!