Question

14
quadrilateral cdef is similar to quadrilateral mnop.
what is the measure of angle mno of the bigger quadrilateral? (note: the quadrilaterals are not drawn to scale.)
a 114° b 24° c 96° d 126°

Explanation:

Step1: Recall similar polygon properties

Corresponding angles of similar quadrilaterals are congruent, and consecutive angles in a parallelogram (these are parallelograms, as opposite sides are equal) are supplementary.

Step2: Identify angle relationship

Angle MNO is consecutive to angle ONP (which corresponds to angle C=66° in the smaller quadrilateral). So $\angle MNO = 180^\circ - 66^\circ$

Step3: Calculate the angle

$\angle MNO = 114^\circ$

Answer:

A. $114^\circ$