Question

solve for x, y, and z 9 pts (4z + 6)° x° 106° 2y°

Explanation:

Step1: Find \(x\)

Use the property of supplementary angles. \(x + 106^{\circ}=180^{\circ}\) (linear - pair of angles).

$$x=180 - 106$$

$$x = 74^{\circ}$$

Step2: Find \(y\)

Use the property of vertical angles. \(2y=106^{\circ}\) (vertical angles are equal).

$$y=\frac{106}{2}$$

$$y = 53^{\circ}$$

Step3: Find \(z\)

Use the property of corresponding angles. \(4z+6=x\). Substitute \(x = 74\) into the equation.

$$4z+6=74$$

$$4z=74 - 6$$

$$4z=68$$

$$z=\frac{68}{4}$$

$$z = 17$$

Answer:

\(x = 74\), \(y = 53\), \(z = 17\)