Question

1. find the value of x.

20)
21)
22)

Explanation:

19)

Step1: Use vertical - angle property

Vertical angles are equal. The angle vertical to the one with measure \(93^{\circ}\) has the same measure. So, we set up the equation \(3x + 18=93\).

Step2: Solve the equation for \(x\)

Subtract 18 from both sides: \(3x=93 - 18\), so \(3x = 75\). Then divide both sides by 3: \(x=\frac{75}{3}=25\).

20)

Step1: Use the fact that the sum of angles around a point is \(360^{\circ}\)

We know that \(296^{\circ}+29^{\circ}+(x - 24)^{\circ}=360^{\circ}\).

Step2: Simplify the left - hand side

First, combine like terms: \(296+29+(x - 24)=360\), which is \(325+x - 24 = 360\), and further simplifies to \(x+301 = 360\).

Step3: Solve for \(x\)

Subtract 301 from both sides: \(x=360 - 301=59\).

21)

Step1: Use the fact that the sum of angles around a point is \(360^{\circ}\)

We have \(62^{\circ}+(2 + 3x)^{\circ}+90^{\circ}+(6x + 2)^{\circ}=360^{\circ}\).

Step2: Combine like terms

\(62+2 + 3x+90+6x + 2=360\), which simplifies to \((3x+6x)+(62 + 2+90 + 2)=360\), so \(9x+156 = 360\).

Step3: Solve for \(x\)

Subtract 156 from both sides: \(9x=360 - 156 = 204\). Then \(x=\frac{204}{9}=\frac{68}{3}\approx22.67\).

22)

Answer:

1. \(x = 25\)
2. \(x = 59\)
3. \(x=\frac{68}{3}\)
4. \(x = 38\)