Question

3 angles of a quadrilaterals are in ratio 2:3:5 and fourth angle is 90degree, find measure of other 3 angles

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

Assumption

Angles are :-

2p , 3p , 5p , 90°

As we know that

${\boxed{\sf\:{Sum\;of\;all\;angles\;of\;Quadrilateral}}}$

= 360°

Hence,

2p + 3p + 5p + 90° = 360°

10p + 90° = 360°

10p = 360° - 90

10p = 270°

${\implies p=\dfrac{270}{10}}$        

p = 27°

${\boxed{\sf\:{Putting\;value\;of\;'p'}}}$

⇒ ∠1 = 2p

⇒ 2(27) = 54°

⇒ ∠2 = 3p

⇒ 3(27) = 81°

⇒ ∠3 = 5p

⇒ 5(27) = 135°

⇒ ∠4 = 90°

Now,

Verification

∠1 + ∠2 + ∠3 + ∠4 = 360°

 54° + 81° + 135° + 90° = 360°

 360°  = 360°

$\Large{\boxed{\bigstar{{Hence\;Verified}}}}$             

Answer 2

$\huge{\underline{\underline{\pink{\mathfrak{AnSwEr :}}}}}$

Angles are 54°, 81°, 135° and 90°

$\huge{\underline{\underline{\green{\mathfrak{Explanation:}}}}}$

one angle is of 90°

And other angles are in ratio of 2:3:5

So, let all angles be 2x, 3x, 5x, 90°

______________________________________

As we know that :

$\large{\sf{2x \: + \: 3x \: + \: 5x \: + \: 90^{\circ} \: = \: 360^{\circ}}}$

Due to angle sum property of quadrilateral.

⇒2x + 3x + 5x + 90 = 360

⇒5x + 5x = 360 - 90

⇒10x = 270

⇒x = 270/10

⇒x = 27°

$\implies {\boxed{\sf{x \: = \: 27^{\circ}}}}$

_________________________________________

Now,

Angle 1 = 2x = 2(27) = 54°

Angle 2 = 3x = 3(27) = 81°

Angle 3 = 5x = 5(27) = 135°

Angle 4 = 90°