Question

pls anyone help me out pls tell answer pls pls
tell with explanation pls ​

Answer 1

GIVEN :-

• ∠A = 75°.
• ∠B = 63°.
• ∠P = 130°.
• ∠N = 97°.

TO FIND :-

• The value of x and y.

SOLUTION :-

In ∆ AOB, By angle sum property of the triangle.

⇒ ∠A + ∠B + ∠AOB = 180°

⇒ 75° + 63° + ∠AOB = 180°

⇒ 138° + ∠AOB = 180°

⇒ ∠AOB = 180° - 138

⇒ ∠AOB = 42°.

Now, By vertically opposite angle property we have,

⇒ ∠AOB = x = 42°.

Now , in quardilateral PONM , By angle sum property,

⇒ ∠P + ∠PON + ∠M + ∠N = 360°

⇒ 130° + x + y + 97° = 360°

⇒ 130° + 42° + 97° + y = 360°

⇒ 269° + y = 360°

⇒ y = 360° - 269

⇒ y = 91°.

Hence the required values of x and y are 42° and 91° respectively.

Answer 2

$\mathbb{\underline{\underline{ANSWER}}}$

$\rm{\underbrace{In ~~∆ ~AOB:-}}$

$\rm∠AOB + 75° + 63° = 180°~~~~~...(ASP ~of~ ∆)$

$\rm∠AOB = 180° - 138°$

$\rm ∠AOB = 42°$

$\rm x = ∠AOB~~~~~...(Vertically~ Opposite~ angle)$

$\rm{\underline{\underline{x = 42°}}}$

$\rm{\underbrace{In~~ □~ MNOP:-}}$

$\rm x + y + 130° + 97° = 360°~~~~~...(ASP ~of~ □)$

$\rm y = 360° - 269°$

$\rm{\underline{\underline{y = 91°}}}$