Question

calculate the value of x in each of the following figures​

Answer 1

$\sf\tt\large{\green {\underline {\underline{⚘\;Question:}}}}$

Find The Value of X in the figure ?

$\sf\tt\large{\ {\underline {\underline{\;answer:}}}}$

➪ Angle B = 120°+ X . [Liner pair found]

a Liner pair = 180°

So, 120°+X = 180°

x= 180°-120°= 60°

Ans:- Angle 1 = 60°

➪ Angle C = 110°+X. [ Linear pair found]

A Liner pair =180 °

So, 110°+X=180°

X = 180°-110°=70°

Ans :- Angle 2 =70°

To Find :-

${ \underline{ \boxed{ \large{ \rm{formula \: (n - 2 \times 180)}}}}}$

∆3 sides -2 × 180°

= 3 - 2× 180°

= 1×180° =180°

:- Given to find interior Angle .

So ,

A+B+C = 180°

x + 60° + 70 ° = 180 °

x + 130 ° = 180 °

x = 180 °-130°

x = 50 °

The present X angle is 50°

Let's Check :-

A+B+C = 180°

= 50°+60°+70° = 180°

= 110°+70° =180°

= 180°=180°

This Statement is correct ✔️

Answer 2

Answer:

• The measure of ∠x is 50°.

Step-by-step explanation:

In the figure, ABC is a triangle, ED is a line segment passing on BC.

We have :

∠EBA + 1 = 180°

• [∵ Linear pair]

120° + 1 = 180°

1(∠ABC) = 180° - 120°

∴ ∠ABC = 60°

Also, we have:

∠ACD + 2 = 180°

• [∵ Linear pair]

2(∠ACB) = 180° - 110°

∴ ∠ACB = 70°

Now, In ΔABC:

∠ABC + ∠ACB + ∠BAC(x) = 180°

• [∵ Angle sum property]

⇒ 60° + 70° + x = 180°

⇒ 130° + x = 180°

⇒ x° = 180° - 130°

∴ x° = 50°

Verification :

• Angle sum property

∠ABC + ∠ACB + ∠BAC(x) = 180°

⇒ 60° + 70° + 50° = 180°

⇒ 130° + 50° = 180°

⇒ 180° = 180°