Question

in exercises 5 - 10, find the value of x. show your steps. (see example 5. 2x° 128° 6. 72° (7x + 24)°

Explanation:

Step1: Identify angle - relationship for exercise 5

Use corresponding - angles property. Corresponding angles formed by parallel lines and a transversal are equal. So, $2x = 128$.

Step2: Solve for $x$ in exercise 5

Divide both sides of the equation $2x = 128$ by 2.
$x=\frac{128}{2}=64$.

Step3: Identify angle - relationship for exercise 6

Use the property of same - side interior angles. Same - side interior angles formed by parallel lines and a transversal are supplementary, i.e., their sum is $180^{\circ}$. So, $72+(7x + 24)=180$.

Step4: Simplify the equation for exercise 6

Combine like terms: $7x+96 = 180$.

Step5: Solve for $x$ in exercise 6

Subtract 96 from both sides: $7x=180 - 96=84$. Then divide both sides by 7, $x = \frac{84}{7}=12$.

Answer:

For exercise 5: $x = 64$
For exercise 6: $x = 12$