Question

WILL GIVE BRAINLIST. PLEASE HELP.​

Answer 1

Answer:

$0$

Step-by-step explanation:

Please refer to the image attached with this answer. Assuming our triangle to be ΔABC and Line AD meeting BC at D.

As we are given that side b = side c

The angle subtended by them ∠B and ∠C must be equal . Let us assume them to be x each . hence

x + x + 52° +31° = 180°

2x + 73° = 180°

2x = 180°- 73°

2x = 107 °

x = 53.5°

Hence in ΔACD

x+ 31°+∠2= 180°

53.5°+31°+ ∠2 = 180°

∠2=180°-84.5°

∠2=95.5°

Also

∠1 + ∠2 = 180°

∠1 + 95.5° = 180°

∠1 = 180°-95.5°

∠1 =84.5°

Now applying Sine rule in ΔABD

$\frac{\sin 52}{12}=\frac{\sin 84.5}{c}$

$\frac{0.7886}{12}=\frac{0.9953}{c}$

$c=\frac{0.9953 \times 12}{0.7886}$

$c=15.14$

Hence we have c as 15.14

as we are given that side c = side b , b=15.14

The properties of any triangle says that the sum of two sides of any triangle is always greater than the third side. Hence

a<b+c

12+2x-6<15.14+15.14

6+2x<30.28

2x<30.28-6

2x<24.28

x<12.14

also side a must be greater than 0

12+2x-6>0

6+2x>0

2x>-6

x>-3

Hence the range of x will be

-3 <x < 12.14