Question

1. what is the measure, in degrees, of the highlighted (middle) angle?

a. 9.3
b. 18.6
c. 65.1
d. 83.7

1. the measures of the angles of a triangle are given.

• the measure of angle a is $(x + 4)$.
• the measure of angle b is twice the measure of angle a.
• the measure of angle c is equal to the measure of angle b.

what is the value of x?

• a. 32

b. 41
c. 86
d. 68

1. a rectangular swimming pool has a length of $2x + 8$ meters and a width of $x + 4$ meters. the perimeter of the pool is 60 meters. what is the width of the pool?

select the correct answer from the drop - down to complete the sentence.
the width of the pool is meters.

• 6
• 10
• 5
• 12

Explanation:

Question 3

Step1: Use the angle - sum property of a straight - line angles

The sum of angles on a straight line is \(180^{\circ}\). So, \(7x + 2x+96.3 = 180\).

Step2: Combine like terms

\(9x+96.3 = 180\).

Step3: Isolate the variable term

Subtract \(96.3\) from both sides: \(9x=180 - 96.3\). Then \(9x = 83.7\).

Step4: Solve for \(x\)

Divide both sides by \(9\): \(x=\frac{83.7}{9}=9.3\).

Step5: Find the measure of the middle angle

The middle angle is \(2x\). Substitute \(x = 9.3\) into \(2x\), we get \(2\times9.3=18.6\).

Step1: Express the measures of angles \(B\) and \(C\) in terms of \(x\)

Given \(\angle A=(x + 4)\), \(\angle B = 2(x + 4)=2x+8\), \(\angle C=\angle B=2x + 8\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x + 4)+(2x + 8)+(2x + 8)=180\).

Step3: Combine like terms

\(x+4+2x + 8+2x+8=180\), \(5x+20 = 180\).

Step4: Isolate the variable term

Subtract \(20\) from both sides: \(5x=180 - 20\), \(5x=160\).

Step5: Solve for \(x\)

Divide both sides by \(5\): \(x=\frac{160}{5}=32\).

Step1: Use the formula for the perimeter of a rectangle

The perimeter of a rectangle \(P = 2(l + w)\), where \(l = 2x+8\) and \(w=x + 4\), and \(P = 60\). So, \(2((2x + 8)+(x + 4))=60\).

Step2: Simplify the equation inside the parentheses

\((2x + 8)+(x + 4)=3x+12\). The equation becomes \(2(3x + 12)=60\).

Step3: Distribute the \(2\)

\(6x+24 = 60\).

Step4: Isolate the variable term

Subtract \(24\) from both sides: \(6x=60 - 24\), \(6x=36\).

Step5: Solve for \(x\)

Divide both sides by \(6\): \(x = 6\).

Step6: Find the width

The width \(w=x + 4\). Substitute \(x = 6\) into \(w\), we get \(w=6 + 4=10\).

Answer:

B. \(18.6\)

Question 4