Question

12. one of the angles of a quadrilateral is right angle. If the sum of other two angle is 135º. Find the 4 angle​

Answer 1

Given :

• One of the angles of a quadrilateral is right angle. If the sum of other two angle is 135°.

To Find :

• Fourth angle = ?

Solution :

• Let fourth angle be 'x'

• One of the angle is 90°.

• And sum of remaining two angles is 135°.

As we know that, the sum of all sides of quadrilateral is 360°

★ According to Question now :

→ ∠1 + ∠2 + ∠3 + ∠4 = 360°

→ 135° + 90° + x = 360°

→ 225 + x = 360°

Substracting 225 from 360 we get :

→ x = 360 - 225

→ x = 135°

• Hence, the measure of fourth angle is 135°.

⠀⠀━━━━━━━━━━━━━━━━━━━━━

V E R I F I C A T I O N :

→ 135° + 90° + x = 360

→ 225° + 135° = 360°

→ 360° = 360°

⛬ LHS = RHS

Hence Verified !

═════════════════════════

Answer 2

$\huge{\boxed{\rm{Correct \: question}}}$

One of the angles of a quadrilateral is right angled . If the sum of other two angle is 135° . Find the 4th angle .

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• One of the angles of a quadrilateral is right angle.

• The sum of other two angle is 135º

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• The measure of 4th angles.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• The measure of 4th angles is 135°

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: first}}}}$

• This question says that there given is quadrilateral . It's one angle is right angled. And we know that a right angle is always equal to 90° . Then the question says that it's 2 angles sum is 135° . After that it ask to find the measure of 4th angle of given quadrilateral.

$\large{\boxed{\boxed{\sf{How \: to \: do \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Procedure \: is \: given \: below \: let's \: see}}}}$

• As we know that the 3 angles of quadrilateral are given . We have to find the 4th angle of the quadrilateral. So, we have to assume the 4th angle of quadrilateral as x. After that putting the values . And we already know that 3 angles are given so we have to write 135° + 90° + x° = 360° . Now we have to solve it we write only 135° here because angle is is equal to angle 2 in this question. And after that we get our final result that is 135° Hence, the given question is solved. Let's do it properly :)

$\large{\boxed{\boxed{\sf{Let's \: do \: it \: properly}}}}$

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

Let the 4th angle of the quadrilateral be ❛x❜

As we know that what is given in the question ⇓

➼ One of the angle of quadrilateral is right angled means 90°

➼ And sum of other 2 angles are 135°

We also know that ⇓

➼ Sum of angles of quadrilateral = 360°

Now according to the question ⇓

☛ < 1 , < 2 , < 3 , < 4 = 360°

{ We know that in this question < 1 is equal to < 2 }

☛ 135° + 90° + x° = 360°

☛ 225° + x° = 360°

☛ x° = 360° - 225°

☛ x° = 135°

Hence, 135° is the 4th angle of given quadrilateral.

$\large{\boxed{\boxed{\sf{Are \: you \: confused \: \: \: \: Yes}}}}$

$\large{\boxed{\boxed{\sf{Don't \: worry \: let's \: verified \: it}}}}$

Verification is given below ⇓

☛ 135° + 90° + 135° = 360°

☛ 225° + 135° = 360°

☛ 360° = 360°

☛ L.H.S = R.H.S

Hope it's helpful to u all !

Thank you guys :)