Given:
A figure of a quadrilateral.
To find:
The measures of angle 1 and angle 2.
Solution:
The given figure has two pairs of congruent adjacent sides. So, the quadrilateral in the figure is a kite.
We know that the diagonals of a kit are perpendicular to each other at the point of intersection.
[tex]m\angle 1=90^\circ[/tex]
According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.
[tex]90^\circ+65^\circ+m\angle 2=180^\circ[/tex]
[tex]155^\circ+m\angle 2=180^\circ[/tex]
[tex]m\angle 2=180^\circ-155^\circ[/tex]
[tex]m\angle 2=25^\circ[/tex]
Therefore, the correct option is C.
