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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.
To find the measures of angle 1 and angle 3 in the kite, we need to first identify some properties of kites:
1. In a kite, the diagonals are perpendicular.
2. The diagonals of a kite intersect at a right angle.
3. The diagonals of a kite bisect each other.
Since angle DAC is given as 39 degrees, we can find angle 1 and angle 3 as follows:
1. Angle 1 is half of angle DAC, since the diagonals bisect each other. Therefore, angle 1 = 39 degrees / 2 = 19.5 degrees.
2. Angle 3 is equal to angle 1, since opposite angles in a kite are congruent. Therefore, angle 3 = 19.5 degrees.
Therefore, m∠1 = 19.5 degrees and m∠3 = 19.5 degrees.