Question

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$\huge\sf\pink{Question}$

D is a point on side BC of ΔABC such that ∠ABC > ∠ACB and AB > AD. Then, which of the following statement is always true?

A)∠ACB > ∠ADC
B)∠ABC > ∠ADC
C)∠ACB < ∠ADC
D)∠ADB < ∠ABC​

$\sf\bold{explanation\: is\: must}$​

Answer 1

Step-by-step explanation:

Given :-

D is a point on side BC of ΔABC such that ∠ABC > ∠ACB and AB > AD.

To find :-

Which of the following statement is always true?

A)∠ACB > ∠ADC

B)∠ABC > ∠ADC

C)∠ACB < ∠ADC

D)∠ADB < ∠ABC

Solution :-

Given that

In ∆ ABC , D is the point on BC such that

∠ABC > ∠ACB

We know that

The sides opposite to the greatest angle is longer

=> AC > AB ---------(1)

and given that

AB > AD ---------(2)

=> ∠ACB > ∠ABD

From (1) &(2)

AC > AB > AD

The angles opposite to the longer sides is largest

=>∠ABC > ∠ACB > ∠ ADC

=> ∠ABC > ∠ ADC

Answer:-

∠ABC > ∠ ADC

Used formulae:-

→ The sides opposite to the greatest angle is longer

→ The angles opposite to the longer sides is largest .

Answer 2

Step-by-step explanation:

C)ZACB < ZADC

it's your answer hope it helps you