Question

KLMN is a square and NM = 8. Solve for the blanks below:

N
M
K
L
TZOKL=
mZMOL =
Perimeter of KLMN =

Answer 1

Perimeter: 32

measure of angle OKL: 45

measure of angle MOL: 90

Explanation:

Things to remember:

- the side of the square are all equal

- vertical angles are congruent

+ ex. MON and KOL; MOL and NOK

- the entirety of the four angles in the center of the square equal 360 degrees

+ ex. MON + MOL + LOK + KON = 360 degrees

- corners of a square equal 90 degrees and since lines MK and LN cut the square in half we can assume that angles like OKL are also cut in half, making them 45 degrees

+ ex. angle NKL (90) = OKL (45) + OKN (45)

- The four triangles in the square are isosceles

If we have the angles of OML and MLO we can find MOL since the angles of a triangle equal 180

OML (45) + MLO (45) + MOL (x) = 180

90 + x = 180

x = 90

Answer 2

see explanation

Explanation:

the angles in a square are right .

the diagonals bisect the angles , then

∠ OKL = 45°

The diagonals are perpendicular to each other , then

∠ MOL = 90°

All sides are congruent , so

perimeter = 4 × NM = 4 × 8 = 32