192 = total beads
necklace + bracelet = 192
Let x equal the number of beads
bracelet = 5x
necklace = x
5x + x = 192
6x = 192
x = 32
It takes 32 beads to make a necklace
<u>Finding x:</u>
We know that the diagonals of a rhombus bisect its angles
So, since US is a diagonal of the given rhombus:
∠RUS = ∠TUS
10x - 23 = 3x + 19 [replacing the given values of the angles]
7x - 23 = 19 [subtracting 3x from both sides]
7x = 42 [adding 23 on both sides]
x = 6 [dividing both sides by 7]
<u>Finding ∠RUT:</u>
We can see that:
∠RUT = ∠RUS + ∠TUS
<em>Since we are given the values of ∠RUS and ∠TUS:</em>
∠RUT = (10x - 23) + (3x + 19)
∠RUT = 13x - 4
<em>We know that x = 6:</em>
∠RUT = 13(6)- 4
∠RUT = 74°
FYI - 14,15,16 are correct.
17. a) 7 (nearest integer), b) 6.8 (nearest tenth)
18. a) 14 (nearest integer), b) 13.8 (nearest tenth)
19. 
--> simplified to = 2
<em>-- let me know if you have any questions regarding this. </em>
answer for this question is 2/19
1 because 5÷3=1 and a remainder of 2 students.
