Math, asked by umajee73, 3 days ago

he angles of a quadrilateral are in the ratio 6: 7 :8:9, then which of the following can be concluded ?
(1) Exactly two angles are obtuse
(2) Two pairs of angles are supplementary
(3) Both (1) and (2)
(4) One of these angles is a right angle.

Answers

Answered by GunvantSingh
1

Answer is (3) Both (1) and (2)

Answered by Syamkumarr
2

Answer:

All the given statements are true except statement 4.

Step-by-step explanation:

Given that the ratios of the angles of a quadrilateral is 6 : 7 : 8 : 9

Let the multiplying factor be 'x'

Therefore, the angles will be 6x, 7x, 8x and 9x

We know that sum of all the interior angles of a quadrilateral is 360°

Therefore 6x + 7x + 8x + 9x = 360°

=> 30x = 360°

=> x = 360/30

=> x = 12°

Therefore, the angles will be 6x= 72°

                                         7x = 84°

                                         8x = 96°

                                         9x = 108°

Therefore, the quadrilateral has angles measuring 72°, 84°, 96° and 108°.

Now, checking the given statements,

(1) 96° and 108° are obtuse angles. Therefore, Statement (1) is True.

(2) As 72° + 108° = 180° and 84° + 96° = 180° Therefore, Statement (2) is True.

(3) As Statements (1) and (2) are True, Statement (3) is True.

(4) As neither of the angles in the quadrilateral is a right angle, Statement (4) is False.

Therefore, All the given statements are true except statement 4.

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