Question

16. CDEF is a square. Find x.
(a) 142°
(b) 92°
(c) 113°
(d) 83°​

Answer 1

Answer:

Option B

Step-by-step explanation:

FD is a diagonal divides angle EDC in equal halves

(i.e.angle FDC and FDE are 45°)

Angle FME and DMN are vertically opposite angles which are equal.

So.Angle DMN = 68°

x°= 68 + 45= 113°

Answer 2

We know, all the angles of a square = 90°

Also, Each diagonal divides the square into two congruent isosceles right triangles.

Therefore, ∠MDN = ∠MDE     [CPCT]

And, ∠MDN = 45°

∠FME = 68°

But, ∠FME = ∠DMN   [vertically opposite angles]

Therefore, ∠DMN = 68°

Now, Consider ΔDMN,

∠DMN + ∠MDN = ∠MNC

68° + 45° = ∠MNC

113° = ∠MNC

Therefore, Option (c) is the correct option..

Hope this helps! Thank you!