Question

The angle of a quadrilateral are given to be (3x), (3x+30),(6x+60),90 find the value of all the angle of quadrilateral​

Answer 1

Answer:

First angle  = 45°

Second angle = 75°

Third angle  = 150°

Fourth angle = 90°

Step-by-step explanation:

The sum of angles of a quadrilateral is 360°.

Given: Angles of a quadrilateral are (3x), (3x+30), (6x+60), 90

So,

(3x) +  (3x+30) + (6x+60) + 90 = 360°

3x + 3x + 30 + 6x + 60 + 90 = 360°

Arrange similar terms

3x + 3x + 6x + 30 + 60 + 90 = 360°

(3 + 3+ 6)x + (30 + 60 +90) = 360°

12x + 180° = 360°

12x = 360° - 180°

12x = 180°

x = 180/12

x = 15

So, first angle = 3(15) = 45°

Second angle = 3(15) + 30 = 45 + 30 = 75°

Third angle = 6(15) + 60 = 90 + 60 = 150°

Fourth angle = 90°

Answer 2

Answer:

Let the quadrilateral be PQRS

<P = 3x

<Q = 3x + 30

<R = 6x + 60

<S = 90

We know that

<P + <Q + <R + <S = 360

3x + 3x + 30 + 6x + 60 + 90 = 360

12x + 180 = 360

12x = 360 - 180

12x = 180

x = 15

So, <P = 3×15 = 45

<Q = 3×15 + 30 = 45 + 30 = 75

<R = 6×15 + 60 = 90

<S = 90

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