Question

find the value of x.​

Answer 1

Answer:

Value of x is 14°.

Step-by-step explanation:

Suppose, ABC is a triangle and O is an angle inside ∆ABC. ∠1 is an angle of ∆AOB. ∠2 is an angle of ∆AOC and ∠3 is an angle of ∆BOC.

We know,

• If any two sides of triangle are equal then their opposite angles are also equal .

So,

In ∆AOB :

⇒∠1 = 40°

In ∆AOC :

⇒∠2 = 36°

In ∆BOC :

⇒∠3 = x

And,

• ∠A = ∠1 + ∠2

⇒ ∠A = 40° + 36°

⇒ ∠A = 76°

• ∠B = 40° + x

• ∠C = 36° + ∠3

⇒ ∠B = 36° + x

Now,

We also know,

✿ Sum of all interior angles of triangle is equal to 180° or also known as "Angle sum property of triangle".

So,

$\implies$ ∠A + ∠B + ∠C = 180°

$\implies$ 76° + 40° + x + 36° + x = 180°

$\implies$ 152° + 2x = 180°

$\implies$ 2x = 180° - 152°

$\implies$ 2x = 28°

$\implies$ x = 28°/2

$\implies$ x = 14°

Therefore,

Value of x is 14°.

Answer 2

$\rm \bigstar \: Solution :$

$\rm \: From \: Figure ,$

$\rm \implies \: OB = OC$

$\rm \implies \angle OCB = \angle OBC$

$\rm \therefore \:\angle OCB = \: x$

$\rm\therefore \angle OBC = x$

$\rm \: Again \: ,$

$\rm\implies \: OA = OC$

$\rm \: So ,$

$\rm \angle OCA = \angle \: OAC = 40 \degree$

$\rm \: \angle AOC = 180 \degree - (40 + 40 \degree)$

$\rm \implies \: 180 \degree - 80 \degree$

$\rm \therefore \angle AOC = 100 \degree$

$\rm \: Again \: ,$

$\rm\implies \: OB = OA$

$\rm \: So ,$

$\rm \angle BAO = \angle \: ABO = 36 \degree$

$\rm \: \angle AOB = 180 \degree - (36+ 36\degree)$

$\rm \implies \: 180 \degree - 72 \degree$

$\rm \therefore \angle AOB= 108 \degree$

$\rm \: Now :$

$\rm \angle BOC= 360 \degree -( 100 + 108 \degree)$

$\rm \implies \: 360 \degree - 208 \degree$

$\rm \therefore \angle BOC = 152 \degree$

$\rm \: So ,$

$\rm \: \implies \angle OCB = x +x +152 \degree$

$\rm \: \implies 2 \: x +152 \degree$

$\rm \: Now \: in \: \angle BOC$

$\rm \: \implies 2 \: x +152 \degree \: = 180 \degree$

$\rm \: \implies 2 \: x = 180 - 152 \degree$

$\rm \: \implies 2 \: x = 28 \degree$

$\rm \: \implies \: x = \dfrac{28}{2}$

$\rm\boxed{\implies \: x =14 \degree}$

$\rm \: \bigstar \: Therefore :$

$\small \text{The value of x in given figure is x = 14 \degree}$