Question

In ΔABC, ∠BAC = (6x + 3)° and ∠ABC = (3x - 6)°. Which of these is ∠BCA? Please answer quickly

Answer 1

QUESTION:

In ΔABC, ∠BAC = (6x + 3)° and ∠ABC = (3x - 6)°. Which of these is ∠BCA?

1. 180° - [(6x + 3)° - (3x - 6)°]

2. 180° - [(6x + 3)° + (3x - 6)°]

3. 180° + (6x + 3)° - (3x - 6)°

4. 180° + (6x + 3)° + (3x - 6)°

ANSWER:

For the given ΔABC, the value of ∠BCA will be 180° - [(6x + 3)° + (3x - 6)°]. (option 2)

Given,

In a ΔABC,

∠BAC = (6x + 3)°,

∠ABC = (3x - 6)°.

To find,

∠BCA.

Solution,

We can see that here, two angles of a triangle ABC are given, which are as follows.

∠BAC = (6x + 3)°,

∠ABC = (3x - 6)°.

We have to find the third angle, ∠BCA.

Now, we know that in any triangle, the sum of all of its three angles is equal to 180°.

So, for the given triangle ABC, we can write,

∠BAC + ∠ABC + ∠BCA = 180°.

Substituting the given values for the angles, we get,

(6x + 3) + (3x - 6) + ∠BCA = 180

On rearranging, to determine ∠BCA, the above equation becomes,

∠BCA = 180° - [(6x + 3)° + (3x - 6)°]

The above equation gives the value of the required ∠BCA.

Therefore, for the given ΔABC, the value of ∠BCA will be 180° - [(6x + 3)° + (3x - 6)°]. (option 2)

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