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.
Since the kite is symmetrical, we know that angles 1 and 3 are congruent. Let's call the measure of angle 1 "x". Since angle DAC is 39 degrees, angle BAC (angle 1 + angle 3) must be 39 degrees. This means that x + x = 39. Simplifying, we have 2x = 39, so x = 19.5. Therefore, m∠1 = m∠3 = 19.5 degrees.
