Question

in the given figure AC is the bisector of angle A if ab is equal to AC ad is equal to CD and angle abc is equal to 75 degree find the value of x and y​

Answer 1

Answer:

1. x° = 30°
2. y° = 120°

Step-by-step explanation:

A) Triangle ABC is an isosceles triangle. Hence,  ∠ABC=∠BAC

  So, 180° = ∠ABC + ∠BAC + ∠ACB

⇒ 180° = 75° + 75° + x°

⇒ x° = 180° - 75° - 75°

⇒ x° = 30°

B) Again, Triangle ADC is a isosceles triangle, where AD=CD.

Also, ∠ACD=∠ACB, since ∠BCD is bisected by line AC.

And ∠ACD=∠CAD = 30°

Now -

180° = ∠ACD + ∠CAD  + ∠ADC

180° = 30° + 30° + y°

y° = 180° - 30° - 30°

y° = 120°