Question

1. linear pair angles x and y form a linear pair. angle x = 3x + 10 angle y = 5x - 30 what is the value of x?

Explanation:

Step1: Recall linear pair property

A linear pair of angles sums to \(180^\circ\). So, \( \text{Angle } x + \text{Angle } y = 180 \).
Substitute \( \text{Angle } x = 3x + 10 \) and \( \text{Angle } y = 5x - 30 \) into the equation:
\( (3x + 10) + (5x - 30) = 180 \)

Step2: Simplify the equation

Combine like terms:
\( 3x + 5x + 10 - 30 = 180 \)
\( 8x - 20 = 180 \)

Step3: Solve for \(x\)

Add 20 to both sides:
\( 8x - 20 + 20 = 180 + 20 \)
\( 8x = 200 \)
Divide both sides by 8:
\( x = \frac{200}{8} = 25 \)

Answer:

\( x = 25 \)