Question

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The angles of a quadrilateral are in the ratio 4: 5: 10: 11. The angles are: solve the problem!!:)

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Answer 1

Answer:

• The angles in a quadrilateral sum up to 360°.
• The angles given here in the ratio form are : 4x, 5x, 10x and 11x.

Hence, 4x + 5x + 10x + 11x = 360

• ⇒ 30x = 360
• ⇒ x = 360/30
• ⇒ x = 12

Hence, the angles = ?

• ⇒ 4x = 4(12) = 48°
• ⇒ 5x = 5(12) = 60°
• ⇒ 10x = 10(12) = 120°
• ⇒ 11x = 11(12) = 132°

• Therefore, the angles are : 48°, 60°, 120° and 132°.

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Important :

• A quadrilateral is a four sided shaped.
• It has 4 vertices.
• Sum of interior angles : 360°
• Perimeter is the sum of all four sides.
• Area = ½×diagonal×(sum of perpendicular heights)

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Answer 2

$\implies \dag \large{\blue{\underline{\underline{\red{\textsf{\textbf{Answer }}}}}}}</p><p>$

$\rm{ \purple{given \: ratio \: of \: angles \: are \: as \: follows}} \\ \: \: \: \: \: \: \large \bold{4:5:10:11}$

$\large \rm{ \pink{now.}} \\ \rm { \red{let \: the \: angles \: be \: (4x)(5x)(10x)and(11x)}}$

ʜᴇʀᴇ ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

$\bold{sᴜᴍ \: ᴏғ \: ᴀʟʟ \: ᴀɴɢʟᴇs \: ᴏғ \: ᴀ \: ǫᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ \: ɪs \: 360°}$

Now we have to find the value of "X"

so,

$\rm \large { \green{(4x +5x + 10x + 11x ) = 360}}$

now on adding these numbers,

we get,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \large{ \green{(30x = 360)}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \huge{ \green{x = \frac{360}{30} }}$

$\: \: \: \: \: \: \: \: \: \: \rm \large{ \green{so \: (x = 12)}}$

so on putting value of X in all angles :

we get,

$\: \: \: \bold{(4x = 4 \times 12 = 48)} \\ \: \: \: \bold{ (5x = 5 \times 12 = 60)} \\ \: \: \: \bold{(10x = 10 \times 12 = 120)} \\ \: \: \: \bold{(11x = 11 \times 12 = 132)}$

hence,

angles are = 48°

=60°

= 120°

=132°