Answer:
C. \(m\angle 1=90^{\circ}\), \(m\angle 2=14^{\circ}\), and \(m\angle 3=76^{\circ}\)
Step-by-step explanation:
We have been given a rhombus. We are asked to find the angles of our given rhombus.
We know that rhombus is a parallelogram, whose all sides are equal.
Since rhombus is parallelogram, so alternate interior angles will be equal. Therefore, measure of angle 2 is 14 degrees.
The diagonals of rhombus are perpendicular bisector of each other, therefore, measure of angle 1 is 90 degrees.
Since diagonals of rhombus are perpendicular bisector of each other, so they divide rhombus into four congruent triangles.
We can find measure of angle 3 using angle sum property.
\(m\angle 3+90^{\circ}+14^{\circ}=180^{\circ}\)
\(m\angle 3+104^{\circ}=180^{\circ}\)
\(m\angle 3+104^{\circ}-104^{\circ}=180^{\circ}-104^{\circ}\)
\(m\angle 3=76^{\circ}\)
Therefore, measure of angle 3 is 76 degrees and option C is the correct choice.
