Question

what is the value of x? (the image shows two intersecting lines at point r, with angles x° and (3x)° adjacent to each other. there are four multiple - choice options: 45, 60, 30, 55)

Explanation:

Step1: Identify angle relationship

The angles \( x^\circ \) and \( 3x^\circ \) are adjacent and form a linear pair, so their sum is \( 180^\circ \).
\[ x + 3x = 180 \]

Step2: Solve for \( x \)

Combine like terms:
\[ 4x = 180 \]
Divide both sides by 4:
\[ x = \frac{180}{4} = 45 \]

Answer:

45