Question

I really need help with this!

Answer 1

Answer:

Step-by-step explanation:

1) in a rhombus, the diagonals bisect each other at the midpoint, forming 4 right angles.

MK = NK + NM

Since MK = 24 and NK = NM, then,

NK = 24/2 = 12

JL = NJ + NL

Since JL = 20 and NJ = NMlL, then,

NL = 20/2 = 10

Looking at triangle LMN, it is a right angle triangle. Applying Pythagoras theorem,

ML^2 = 10^2 + 12^2 = 100 + 144 = 244

ML = √244 = 15.62

Since all the sides of the rhombus are equal, then

MJ = ML = 15.62

Angle KNL = angle JML = 90 degrees. This is so because the diagonals are perpendicular)

Angle KJL = 90 - angle MJL

Angle KJL = 90 - 50 = 40 degrees.

Since the opposite angles of the rhombus are equal,

Angle MLK = angle angle MJK = 50 + 40 = 90 degrees

2) since all the sides of a rhombus are equal,

5x + 16 = 9x - 32

9x - 5x = 32 + 16

4x = 48

x = 48/4 = 12

Since PQ = NR = 5x + 16, then

PQ = 5×12 + 16 = 60 + 16

PQ = 76

3) Triangle XYZ is an isosceles triangle. This means that its base angles, XZY and ZXY are equal. The sum of angles in a triangle is 180 degrees. Therefore,

Angle XZY + angle ZXY = 180 - 136

Angle XZY + angle ZXY = 44

Angle XZY = 44/2 = 22

Therefore,

10x - 8 = 22

10x = 22 + 8 = 30

x = 30/10 = 3