Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
On the kite, vertex A at the top, vertex B at the right, vertex C at the bottom, and vertex D at the left. Side A B is marked congruent to side A D. Side D C is marked congruent to side B C. Diagonal A C and B D are drawn.<br/>Angle D A C is 39 degrees.
Find m∠1
and m∠3
in the kite. The diagram is not drawn to scale.
(2 points)
To find m∠1 and m∠3 in the kite, we need to use the properties of kites.
In a kite, the diagonals are perpendicular bisectors of each other. This means that diagonal AC bisects angle A and angle C, and diagonal BD bisects angle B and angle D.
Since angle DAC is 39 degrees, angle 1 is half of angle DAC.
m∠1 = 1/2 * 39 degrees
m∠1 = 19.5 degrees
Similarly, angle BDC is also 39 degrees, so angle 3 is half of angle BDC.
m∠3 = 1/2 * 39 degrees
m∠3 = 19.5 degrees