Given:
The figure of a rhombus.
To find:
The measure of angle 1.
Solution:
First label the vertices of the rhombus as shown in the below figure.
We know that the opposite angles of a rhombus are congruent and the diagonals of a rhombus bisect each vertex angle.
[tex]m\angle ABD=m\angle CBD=30^\circ[/tex] (Diagonal BD is the angle bisector)
Now,
[tex]m\angle ABC=m\angle ABD+m\angle CBD[/tex]
[tex]m\angle ABC=30^\circ+30^\circ[/tex]
[tex]m\angle ABC=60^\circ[/tex]
We know that the consecutive angles of a rhombus are supplementary. It means the sum of each pair of consecutive angles is 180 degrees.
[tex]m\angle BAD+m\angle ABC=180^\circ[/tex]
[tex]m\angle 1+60^\circ=180^\circ[/tex]
[tex]m\angle 1=180^\circ-60^\circ[/tex]
[tex]m\angle 1=120^\circ[/tex]
Therefore, the measure of angle 1 is [tex]m\angle 1=120^\circ[/tex].
