solve for x.
9)
10) ( tb = 9 )
( by = -1 + x )
11)
12)
find the measure indicated.
13) find ( mangle srt )
14) ( my = -2 + 8x )
( mk = 13x + 5 )
find ( my )
15) find ( mangle z )
16) find ( kl )

Question

Accepted Answer

### Problem 9
# Explanation:
## Step1: Use rhombus opposite angles
In a rhombus, opposite angles are equal, so $8x + 2 = 50$.
## Step2: Isolate x term
Subtract 2 from both sides: $8x = 50 - 2 = 48$.
## Step3: Solve for x
Divide by 8: $x = \frac{48}{8}$.
# Answer:
$x=6$

---

### Problem 10
# Explanation:
## Step1: Use rhombus diagonal bisector
In a rhombus, diagonals bisect each other, so $BV = TB$.
## Step2: Substitute given values
$-1 + x = 9$.
## Step3: Solve for x
Add 1 to both sides: $x = 9 + 1$.
# Answer:
$x=10$

---

### Problem 11
# Explanation:
## Step1: Sum of rhombus interior angles
Rhombus interior angles sum to $360^\circ$, so $2(8x-5) + 95 + 115 = 360$.
## Step2: Simplify the equation
Calculate constants: $2(8x-5) + 210 = 360$ → $16x - 10 = 360 - 210 = 150$.
## Step3: Isolate x term
Add 10 to both sides: $16x = 150 + 10 = 160$.
## Step4: Solve for x
Divide by 16: $x = \frac{160}{16}$.
# Answer:
$x=10$

---

### Problem 12
# Explanation:
## Step1: Use rhombus congruent sides
All sides of a rhombus are equal, so $2x + 4 = 18$.
## Step2: Isolate x term
Subtract 4 from both sides: $2x = 18 - 4 = 14$.
## Step3: Solve for x
Divide by 2: $x = \frac{14}{2}$.
# Answer:
$x=7$

---

### Problem 13
# Explanation:
## Step1: Use rhombus congruent sides
Rhombus sides are equal, so $45x = 46x - 1$.
## Step2: Isolate x term
Subtract $45x$ from both sides: $0 = x - 1$.
## Step3: Solve for x
$x = 1$.
## Step4: Calculate $\angle SRT$
Substitute $x=1$: $m\angle SRT = 46(1) - 1$.
# Answer:
$m\angle SRT=45^\circ$

---

### Problem 14
# Explanation:
## Step1: Use rhombus diagonal bisector
Diagonals bisect each other, so $MY = KY$.
## Step2: Substitute given values
$-2 + 8x = 13x + 5$.
## Step3: Isolate x terms
$-2 - 5 = 13x - 8x$ → $-7 = 5x$.
## Step4: Solve for x
$x = \frac{-7}{5} = -1.4$.
## Step5: Calculate MY
Substitute $x=-1.4$: $MY = -2 + 8(-1.4) = -2 - 11.2$.
# Answer:
$MY=-13.2$

---

### Problem 15
# Explanation:
## Step1: Sum of rhombus interior angles
Rhombus interior angles sum to $360^\circ$, so $m\angle Z + (7x-4) + (5x+20) + 105 = 360$.
## Step2: Simplify x terms
Combine like terms: $m\angle Z + 12x + 121 = 360$.
## Step3: Use rhombus consecutive angles
Consecutive angles are supplementary, so $7x - 4 + 105 = 180$.
## Step4: Solve for x
$7x + 101 = 180$ → $7x = 79$ → $x = \frac{79}{7} \approx 11.29$.
## Step5: Find $m\angle Z$
$\angle Z$ is supplementary to $5x+20$: $m\angle Z = 180 - (5(\frac{79}{7}) + 20) = 180 - (\frac{395}{7} + \frac{140}{7}) = 180 - \frac{535}{7} = \frac{1260-535}{7}$.
# Answer:
$m\angle Z=\frac{725}{7}\approx103.57^\circ$

---

### Problem 16
# Explanation:
## Step1: Use rhombus consecutive angles
Consecutive angles are supplementary, so $(x+3) + (2x-4) = 180$.
## Step2: Simplify the equation
$3x - 1 = 180$.
## Step3: Isolate x term
$3x = 180 + 1 = 181$.
## Step4: Solve for x
$x = \frac{181}{3} \approx 60.33$.
## Step5: Calculate KL
$KL = x + 3 = \frac{181}{3} + 3 = \frac{181+9}{3}$.
# Answer:
$KL=\frac{190}{3}\approx63.33$

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QUESTION IMAGE

Question

Explanation:

Problem 9

Step1: Use rhombus opposite angles

Step2: Isolate x term

Step3: Solve for x

Step1: Use rhombus diagonal bisector

Step2: Substitute given values

Step3: Solve for x

Step1: Sum of rhombus interior angles

Step2: Simplify the equation

Step3: Isolate x term

Step4: Solve for x

Answer:

Problem 10