2n+8 maybe try that i dont get the question..kinda confusing
Answer:
x = 8
Step-by-step explanation:
Δ TSU and Δ TRV are similar , thus the ratios of corresponding sides are equal, that is
= 
, substitute values
= 
= 
( cross- multiply )
3x = x + 16 ( subtract x from both sides )
2x = 16 ( divide both sides by 2 )
x = 8
<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°
