I’m sorry if I answered too late. Good luck.
5.) The diagonal splits the rhombus into 2 triangles. It says it's a rhombus, and the thing about a rhombus is that all sides are congruent, or of the same length. All angles of a triangle have a sum of 180°, meaning that your equation here is [tex]73 + 2x = 180[/tex].
--> x=53.5 degrees.
This means that angles 1-4 all have a measure of 53.5°. The sum of all the angles is 360°, so you know your answer is correct.
6.) As I mentioned before, all sides in a rhombus are congruent. This means that the 2 bisectors are perpendicular and that m∠1 = 90°. m∠4 corresponds to 25°, so it has the same measure. Because all triangles have 180 degrees total, [tex]25 + 90 + x = 180 --> x = 65[/tex]. m∠3 and m∠2 are 53°.
7.) Using the same method as before, [tex]20+90+x=180-->x=70[/tex]. This means that mm∠1 = m∠3 = m∠4 = 70° and m∠2 = 90°.
8.) [tex]39+90+x=180--> x=51[/tex], m∠1= m∠2= 51°. mm∠3 = m∠4=39°.
9.)
a.) 16
b.) 12
c.) Use the Pythagorean Theorem. [tex]12^2+16^2=c^2 → c^2 = 400 → c= 20[/tex]
d.) OX is half the diagonal, so it is 10 units long.
e.) m∠1 and m∠2 have a sum of 90°. If m∠1=53°, then m∠2=37°.
f.) m∠LON=90° because LMNO is a rectangle.
g.) m∠3=37° because it corresponds to m∠2.
h.) m∠4=53° because it corresponds to m∠1.
