Option D:
m ∠2 = 27°, m ∠3 = 90°
Solution:
Given ABCD is a rhombus.
Measure of ∠1 = 27°
To find the measures of ∠2 and ∠3:
By the property of rhombus,
Diagonals bisect the angles.
Therefore, ∠1 = ∠2
Measure of ∠2 = 27°
Again by the property of rhombus,
Diagonals bisect each other at right angles.
Right angle = 90°
Here ∠3 is bisecting angle of the diagonals.
Therefore, measure of ∠3 = 90°.
So, Option D is the correct answer.
Hence m ∠2 = 27°, m ∠3 = 90°.