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 TOMORRIW. PLS ANS. PLS DON'T GIVE WRONG ANSWERS

Answer 1

Explanation:

In a rectangle KLMN, if the diagonals KM and LN intersect at O, then KO = ON

GIVEN

KO = 4y+6

ON = 3y+11

Equate

4y+6 = 3y+11

Collect like terms

4y-3y = 11-6

y = 5

KO = 4(5)+6

KO = 20+6

KO = 26

Note that KO = OM = LO = ON = 26

Hence ON = 26

For diagonal KM,

KO+OM = KM

KM = 26+26

KM = 52

LN = LO+ON

LN = 26+26

LN = 52

From.the digram, ∆KON is isosceles triangle hence <KON = KNO =32°

<KON = 180-(32+32)

<KON = 180-64

<KON = 116°

<ONM = 90-32

<ONM = 58°

∆ONM is also an isosceles triangle,

<ONM = <OMN = 58°

Hence <KMN = 58°