Answer: Choice c. 39; 51
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Explanation:
Using the SSS congruence theorem, we can show that triangle ABC is congruent to triangle ADC. This in turn means that angle BAC is congruent to angle DAC as these are corresponding angles.
So angle 1 is 39 degrees.
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For any kite, the diagonals always are perpendicular (this can be proven using a similar idea as shown above, but a bit more steps are needed). This means they meet at a right angle, and angle 2 is 90 degrees.
Let point E be the intersection point of the diagonals.
Since angle AEB is 90, this makes angle AED also 90.
Focus entirely on triangle AED. This is a right triangle.
In this triangle, A = 39, E = 90, and D is unknown
Let's find angle D
A+E+D = 180
39+90+D = 180
129+D = 180
D = 180 - 129
D = 51
Angle D is 51 degrees, which also means angle ADB = 51 degrees. This is the measure of angle 3.
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We found that
- angle 1 = 39 degrees
- angle 3 = 51 degrees
Therefore, the final answer is choice C
