Question

question 4 of 10
if mnop is a rectangle, and m∠mon = 60°, what is the value of x?
a. 30
b. 60
c. 90
d. 45
e. 120
f. cannot be determined

Explanation:

Step1: Diagonals in rectangle bisect each other

Diagonals MO and NP intersect at S, so SM=SO=SN=SP.

Step2: ∠MON=60° implies △NOS is equilateral

OS=ON (half-diagonals equal), ∠MON=60°, so OS=ON=NS=a.

Step3: Use Law of Cosines in △NSM

NM=b=√3 a (from rectangle sides), SN=SM=a. NM²=SN²+SM²-2·SN·SM·cosx.

Step4: Solve for x

(√3 a)²=a²+a²-2a² cosx → 3a²=2a²-2a² cosx → cosx=-1/2 → x=120°.

Answer:

E. 120