Question

two angles intersect below. what is the value of x? two angles intersect below. what is the value of x?

Explanation:

First Diagram (with 127° angle)

Step1: Identify vertical angles or supplementary angles

When two lines intersect, vertical angles are equal, and adjacent angles are supplementary (sum to 180°). Here, the 127° angle and \( x^\circ \) are adjacent and form a linear pair, so they are supplementary.

Step2: Set up the equation

The sum of supplementary angles is \( 180^\circ \), so \( 127 + x = 180 \).

Step3: Solve for \( x \)

Subtract 127 from both sides: \( x = 180 - 127 = 53 \).

Second Diagram (with 93° angle)

Step1: Identify angle relationship

When two lines intersect, adjacent angles on a straight line are supplementary (sum to 180°). The 93° angle and \( x^\circ \) are adjacent and form a linear pair, so they are supplementary.

Step2: Set up the equation

The sum of supplementary angles is \( 180^\circ \), so \( 93 + x = 180 \).

Step3: Solve for \( x \)

Subtract 93 from both sides: \( x = 180 - 93 = 87 \).

Answer:

For the first diagram: \( x = 53 \)
For the second diagram: \( x = 87 \)