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