Question

In a rectangle KLMN, the diagonals KM and LN intersect at O. (i) If KO = 4y + 6 and ON = 3y + 11, find the lengths of its diagonals. (ii) If ∠NKM = 32°, find ∠KON and ∠KMN. GUYS, IT'S VERY URGENT. I HAVE TO SUBMIT TOMORROW. PLS ANS. PLS DON'T GIVE WRONG ANSWERS

Answer 1

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Explanation:

Answer 2

1). Length of diagonals = 52

2). m∠KON = 103°, m∠KMN = 45°

Explanation:

KLMN is a rectangle.

Diagonals KM and LN intersect at point O.

1). Since, diagonals of the rectangle equally bisect each other.

KM = 2(KO)

KM = 2(4y + 6)

And LN = 2(ON)

LN = 2(3y + 11)

Since, length of diagonals of a rectangle are equal in measure.

2(4y + 6) = 2(3y + 11)

4y + 6 = 3y + 11

4y - 3y = 11 - 6

y = 5

Therefore, length of diagonals = 2(3y + 11)

= 2(15 + 11)

= 52 units

2). m∠NKM = 32°

Since, m∠KNM = 90° [internal angle of a rectangle]

And diagonal LN bisects this angle,

m∠KNO = 45°

In ΔKNO,

m(∠NKM) + m(∠KNO) + m(KON) = 180°

32° + 45° + m∠KON = 180°

m∠KON = 180° - 77°

= 103°

Since, m∠KMN =
`(1)/(2)`(m∠LMN)

m∠KMN =
`(1)/(2)(90)` = 45°