The quadrilateral below is a rhombus. Find a measure of each of the missing angles I think I got the 38 degree angles right

∡1 ≅ ∡4 ≅ ∡6 (all are 38°) and

∡2 ≅ ∡3 ≅ ∡5 ≅ ∡7 (all are 52°) and

∡8 is 90°

Step-by-step explanation:

in a rhombus, diagonals form 90° angles

so you can find the m∡7 by adding 38 and 90, then subtracting from 180 to get 52°

also, in a rhombus there are 2 pair of parallel sides which means:

∡1 ≅ ∡4 ≅ ∡6 (all are 38°) and

∡2 ≅ ∡3 ≅ ∡5 ≅ ∡7 (all are 52°) and

∡8 is 90°

Answers:

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.

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

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

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.

16 kids because 2 times 8 equals 16

hreryryrranswer:

step-by-step explanation: