Question

If AC is the bisector of angle A and angle C and angle 1 equal to angle 3 , show that angle A equal to angle C​

Answer 1

Answer:

according to vertically opposite angle angle A is equal to angle C

Answer 2

Answer:

In △ABC,

⇒ AB=AC [ Given ]

⇒ ∠ABC=∠ACB [ Base angles of equal sides are also equal. ]

⇒ ∠ABC=75

∴ ∠ACB=75

⇒ ∠ABC+∠ACB+∠BAC=180

⇒ 75 +75 +x=180

⇒ 150 +x=180

⇒ x=30 .

It is given that, AC bisects ∠A

∴ ∠BAC=∠CAD

∴ ∠CAD=30

In △ACD,

⇒ AD=CD [ Given ]

⇒ ∠CAD=∠ACD [ Base angles of equal sides are also equal. ]

∴ ∠ACD=30

⇒ ∠CAD+∠ACD+∠CDA=180

⇒ 30 +30 +y=180

⇒ 60 +y=180

⇒ y=120

∴ The value of x and y are 30 and 120

Step-by-step explanation:

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