Question

Three angles of a quadrilateral are in the ratio 2:3:5 and the fourth angle is 90 find the measures of the other three angles

Answer 1

Heya mate,Here is ur answer

Given : Three angles are in the ratio 2:3:5

Let the common ratio be x.

So, angle 1=2x

angle 2 =3x

Angle 3 =5 x

Angle 4=90°

$<b><u>Using angle sum property of quadrilateral</u></b>$

Angle 1+angle 2 +angle 3 +angle 4 =360°

2x+3x+5x+90°=360°

10x+90°=360°

10x=360°-90°

10x=270°

x=270°/10

x=27°

So, angle 1 =2×27

=54

angle 2 =3×27

=81

angle 3 =5×27

=135

Warm regards

@Laughterqueen

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Answer 2

Ello there!

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Question: Three angles of a quadrilateral are in the ratio 2:3:5 and the fourth angle is 90 find the measures of the other three angles.

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Pre-requisite Knowledge for answering this question.

• All the angles of a quadrilateral add up to 360° (ASP of a quadrilateral)

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Answer

Angles are,

2x, 3x, 5x and 90°

→ In a quadrilateral, the sum of all angles = 360°

Therefore,

2x + 3x + 5x + 90° = 360°

10x + 90° = 360°

         10x = 360° - 90

         10x = 270°

             x = 270°/10

           x = 27°

→ Now, we substitute the value of 'x' in 2x, 3x, and 5x

∠1 = 2x = 2(27) = 54°

∠2 = 3x = 3(27) = 81°

∠3 = 5x = 5(27) = 135°

∠4 = 90°

Therefore all angles are found!

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Not sure with the answer?

There is cool method to check whether the angles you have obtained in the quadrilateral are correct or not. If you add up all angles of the quadrilateral, you must get 360° if you dont you can recheck the answer. Lets try it with the answer I've obtained.

∴  ∠1 + ∠2 + ∠3 + ∠4 = 360°

   54° + 81° + 135° + 90° = 360° (add the angles on LHS)

                             360°  = 360°

                         LHS = RHS

Therefore the angles found are correct!

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#AimBeBrainly