Question

*Fill in the blank: In a ∆ABC , if ∠ABC = ∠BAC + ∠ACB then the value of ∠ABC will be _______.*

1️⃣ 90⁰
2️⃣ 180⁰
3️⃣ 120⁰
4️⃣ 45⁰​

Answer 1

Answer:

1. 90°

Step-by-step explanation:

Provided:-

∠ABC = ∠BAC + ∠ACB

We know:-

∠ABC + ∠BAC + ∠ACB = 180°

∠ABC + ∠ABC = 180°

2 ∠ABC = 180°

∠ABC = 90°

Answer 2

Answer:

The value of the ∠ABC is 90°.

Step-by-step explanation:

Given:- In a ΔABC, ∠ABC = ∠BAC + ∠ACB.

To find:- The value of the ∠ABC.

According to the question,

∠ABC = ∠BAC + ∠ACB . . . . . (1)

In a ΔABC,

The sum of all the angles of a triangle is $180^0$.

⇒ ∠ABC $+$ ∠BAC $+$ ∠ACB = $180^0$

⇒ ∠ABC + ∠ABC = 180° (From 1)

⇒ 2∠ABC = 180°

⇒ ∠ABC = 180/2

⇒ ∠ABC = 90°

Thus, the value of the ∠ABC is 90°.

Therefore, option (1) is correct.

Clearly, rest of the other options are incorrect.

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