Question

if 3 angles of a parrlogram are in the ratio 2:3:4and the fourth angle =90 degree find all angles

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Answer 1

Answer:

Step-by-step explanation:

3 angles of a parallelogram are in the ratio 2:3:4

So let the angles are 2x,3x and 4x and 4th is 90deg

so 2x+3x+4x+90=360

9x=360-90=270

x=270/9=30

Thus the  4 angles are

60,90,120 and 90 degree

NB: This a quadrilateral but not parallelogram because if any angle of parallelogram is 90 then it is a rectangle with all angles 90 degree

Answer 2

Given :-

• Three angles of parallelogram are in ratio 2:3:4.
• Fourth angle of parallelogram is 90°.

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To find:-

• All angles of parallelogram.

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$\color{magenta}{\large\underline{\underline\mathtt{SolutioN}}}$

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Let the three angles of parallelogram be 2x , 3x and 4x.

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We know that,

Sum of all angles of any quadrilateral is 360°.

Parallelogram is a quadrilateral. So,

Sum of all angles of parallelogram is 360°.

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According to question:-

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$\tt⇒2x + 3x + 4x + 90°= 360° \\ \tt\ ⇒9x + 90° = 360° \\ \tt⇒9x = 360° - 90° \\ \tt ⇒9x = 270° \\ \tt ⇒x = \frac{270°}{9} \\ \tt⇒x = 30°$

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✣ First angle:-

$\tt⇒2x = 2 \times 30° \\ \tt⇒60°$

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✣ Second angle:-

$\tt⇒3x = 3 \times 30° \\ \tt⇒90°$

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✣ Third angle:-

$\tt⇒4x = 4 \times 30° \\ \tt⇒120°$

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✣ Fourth angle:-

$\tt⇒90°$

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