Answers:
- angle 1 = 52 degrees
- angle 2 = 52 degrees
- angle 3 = 38 degrees
- angle 4 = 38 degrees
- angle 5 = 38 degrees
- angle 6 = 52 degrees
- angle 7 = 52 degrees
- angle 8 = 90 degrees
In other words, angles 3,4,5 are 38 degrees each. Angles 1,2,6,7 are 52 degrees each. Angle 8 is 90 degrees.
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Step-by-step explanation:
The 38 degree angle on the diagram and the angle 4 are alternate interior angles. For any rhombus, the opposite sides are parallel, meaning alternate interior angles are congruent. So you have the correct value for angle 4. Unfortunately, your other answers are incorrect.
The diagonals of any rhombus are always perpendicular. That means the four smaller triangles that make up the rhombus are all right triangles. From that, angles 2 and 4 are complementary, so,
(angle 2) + (angle 4) = 90
(angle 2) + (38) = 90
angle 2 = 90 - 38
angle 2 = 52 degrees
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A useful property about rhombuses is that the diagonals always bisect the interior angles. In other words, the diagonals cut the interior angles in half.
This means....
- angle 1 = angle 2
- angle 3 = 38 degrees
- angle 4 = angle 5
- angle 6 = angle 7
Since we found angle 2 = 52, this means angle 1 = 52 as well.
Since angle 4 = 38, this makes angle 5 = 38
You should find that angle 7 adds to the 38 degree angle to get 90, since they are complementary angles. So angle 7 is 52 degrees. Note how it's congruent to angle 2, which is an alternate interior angle pair.
From angle 7 = 52, we can see that angle 6 = 52.
Finally, angle 8 = 90 degrees because the diagonals are perpendicular to one another for any rhombus.