Question

find the value of x.
5.
(3x + 6)°
81°
6.
(6x - 11)°
155°
8.
(4x + 60)°
(x + 15)°
(8x)°
(10x - 32)°

Explanation:

Step1: Identify angle - relationship for problem 5

Vertical angles are equal. So, \(3x + 6=81\).

Step2: Solve the equation for \(x\) in problem 5

Subtract 6 from both sides: \(3x=81 - 6=75\). Then divide both sides by 3: \(x = \frac{75}{3}=25\).

Step3: Identify angle - relationship for problem 6

Corresponding angles are equal. So, \(6x-11 = 155\).

Step4: Solve the equation for \(x\) in problem 6

Add 11 to both sides: \(6x=155 + 11=166\). Then divide both sides by 6: \(x=\frac{166}{6}=\frac{83}{3}\approx27.67\).

Step5: Identify angle - relationship for problem 8

Vertical angles are equal. So, \(4x + 60=x + 15\).

Step6: Solve the equation for \(x\) in problem 8

Subtract \(x\) from both sides: \(4x-x+60=x - x+15\), which gives \(3x+60 = 15\). Then subtract 60 from both sides: \(3x=15 - 60=-45\). Divide both sides by 3: \(x=-15\).

Answer:

For problem 5: \(x = 25\)
For problem 6: \(x=\frac{83}{3}\)
For problem 8: \(x=-15\)