Question

angles of a quadrilateral are (x+1), (5x + 4), (x – 2) and (3x + 7). Find all the angles of the quadrilateral.
Also tell the type of quadrilateral.

Answer 1

Answer:

Sum of all angles in a quadrilateral = 360°

x+1 + 5x+4 + x-2 + 3x+7 = 360°

10x+10=360°

10x=350°

x=35°

Therefore, the angles are 36°, 179°, 33°, 112°.

Since none of the angles is supplementary or equal, the quadrilateral would not be any special quadrilateral i.e., a general quadrilateral.

Answer 2

Answer:

Given,

angles of a quadrilateral are (x+1), (5x+4), (x-2) and (3x+7)

A.T.Q,

(x+1) + (5x+4) + (x-2) + (3x+7) = 360

(angle sum property of a quadrilateral)

or, x+5x+x+3x+1+4-2+7 = 360

or, 10x+12-2 = 360

or, 10x+10 = 360

or, 10x = 360-10

or, 10x = 350

or, x = 350/10

or, x = 35

Therefore, all the angles of a quadrilateral are as follows :-

1) x+1 = 35+1 = 36°

2) 5x+4 = 5×35+4 = 175+4 = 179°

3) x-2 = 35-2 = 33°

4) 3x+7 = 3×35+7 = 105+7 = 112°

Answer :- It is a general quadrilateral because none of the angles are supplementary or equal, so this is not a special type of quadrilateral.