A stage technician is aiming two spotlights whose beams form straight lines on a diagram. In the figure, lines and intersect. The angle between the upward ray of line and the rightward ray of line measures . The angle between the upward ray of line and the leftward ray of line measures . What is the value of ?

Solution available with step-by-step explanation

SAT Lines, Angles & Triangles Question 34 | Free SAT Prep | Aniko

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Question 34·Easy·Lines, Angles, and Triangles

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A stage technician is aiming two spotlights whose beams form straight lines on a diagram. In the figure, lines $m$ and $n$ intersect.

The angle between the upward ray of line $n$ and the rightward ray of line $m$ measures $132^\circ$ . The angle between the upward ray of line $n$ and the leftward ray of line $m$ measures $x^\circ$ .

What is the value of $x$ ?

When a diagram shows two adjacent angles forming a straight line, treat them as a linear pair: their measures add to $180^\circ$ . Set up $x + (\text{given angle}) = 180$ and subtract to find $x$ .

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Identify the angle relationship

The two angles share a side, and their other sides form a straight line, so they make a linear pair.

Set up the equation

For a linear pair, the measures add to $180^\circ$ . Write $132 + x = 180$ .

Isolate $x$

Subtract $132$ from $180$ to get $x$ .

Desmos Guide

Compute the supplement

In Desmos, enter 180-132.

Interpret the result

The value returned is $x$ , the angle that forms a linear pair with $132^\circ$ .

Step-by-step Explanation

Use the linear-pair relationship

Because the two angles lie on a straight line (they form a linear pair), their measures sum to $180^\circ$ :

132 + x = 180

Solve for $x$

Subtract $132$ from both sides:

x = 180 - 132 = 48

So, the value of $x$ is $48$ .

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation