Question

In the given figure, AB divides ∆DAC in the ratio 1:3 and AB = DB. The value of x is​

Answer 1

Step-by-step explanation:

REFER THE ATTACHMENT

Answer 2

Answer:

The value of x is 90°.

Step-by-step explanation:

We are given that AB divides ∠ DAC in the ratio 1 : 3 and AB is equal to DB.

We have to determine the value of x.

As it is given in the question that AB divides ∠ DAC in the ratio 1 : 3, that means; ∠DAB/∠BAC = 1/3

∠BAC= 3∠DAB

Let ∠DAB = y, then the value of ∠BAC = 3y ------------- [equation 1]

Now, after observing the figure, it is clear that;

∠CAE + ∠BAC + ∠BAD = 180° {beacuse of linear pair}

→ 108° + 3y + y = 180°

→ 4y = 180° - 108°

→ 4y = 72°

→ y = 72\°/4 = 18°

This means that ∠BAD = y = 18° and ∠BAC = 3y = 3 × 18 = 54°.

Now, as it is given that AB = DB, which means that ∠BDA = ∠BAD {because equal sides have equal opposite angles}

Now, in △BAD, applying angle sum property of the triangle we get;

∠BDA + ∠BAD + ∠ABD = 180°

18° + 18° + ∠ABD = 180°

∠ABD = 180° - 36° = 144°

Now, it is stated that the sum of interior angles is equal to the exterior angle, that means;

∠BAC + ∠BCA = ∠ABD

→ 54° + x = 144°

→ x = 144° - 54° = 90°

Hence, the value of x is 90°.

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