Answer:
Angle 1 = 90°, angle 2 = 54°, angle 3 = 36°, angle 4 = 54°.
Step-by-step explanation:
The given shape is a kite.
The diagonals of a kite are perpendicular to one another, therefore angle 1 is necessarily 90°.
Angle 4 exists in the same triangle as the angle measuring 36 degrees and an angle measuring 90 degrees (as it is also formed by the two diagonals). Thus, since the sum of all angles in a triangle is 180 degrees, angle 4 is equal to (180 - 90 - 36)° = 54°.
Angles 4 and 2 are both the base angles in the same isosceles triangle, therefore they are equal. Thus, angle 2 is also equal to 54°.
Finally, the main diagonal of a kite is also an angle bisector. Thus, angle 3 is equal to the angle measuring 36°.
