In rectangle LMNO, LN = 4x - 12, and OM = 20. Find the value of x\'. The diagona

Question

In rectangle LMNO, LN = 4x - 12, and OM = 20. Find the value of x'. The diagonals of rhombus WXYZ intersect at A. If m WAX = (9x - 9) degree, find the value of 'x' m MLO In rhombus LMNO, the diagonals intersect at X. If m LMO = 32 degree, find m MLO. Determine if the following statements are TRUE or FALSE. If false, provide a counterexample. TRUE or FALSE Counterexample: Every quadrilateral is a parallelogram. TRUE or FALSE Counterexample: If quadrilateral ABCD is a parallelogram, then AB || CD. TRUE or FALSE Counterexample: If both pairs of opposite angles in a quadrilateral are congruent, then the quadrilateral is a parallelogram. TRUE or FALSE Counterexample: If MNOP is a rectangle, then it is a parallelogram.

Explanation / Answer

14.

In a reactangle opposite sides are equal:

LN = 4x-12, OM = 20
So, 4x-12=20
4x=32
x=8

The value of x=8

15. In any rhombus, the diagonals (lines linking opposite corners) bisect each other at right angles (90°). That is, each diagonal cuts the other into two equal parts, and the angle where they cross is always 90 degrees.
So, 9x-9=90
x=11

16. Sides of rhombus are equal. So, LMO = LOM , and therefore, LOM = 32

Hence, in triangle LMO we have 32+32+angle MLO = 180 ( sum of angles in trinalge is 180)

Hence, angle (MLO) = 116

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