Two hiking trails intersect at point , forming four angles. One of the angles measures . The angle adjacent to this angle that forms a straight line with it is labeled . What is the value of ?

Solution available with step-by-step explanation

SAT Lines, Angles & Triangles Question 10 | Free SAT Prep | Aniko

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Question 10·Easy·Lines, Angles, and Triangles

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Two hiking trails intersect at point $P$ , forming four angles. One of the angles measures $47^\circ$ . The angle adjacent to this $47^\circ$ angle that forms a straight line with it is labeled $y^\circ$ . What is the value of $y$ ?

When a problem says two adjacent angles form a straight line, immediately use the supplementary relationship: their measures add to $180^\circ$ . Set up $\text{given} + \text{unknown} = 180$ and subtract.

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Identify the relationship

An angle and its adjacent angle that make a straight line always add to $180^\circ$ .

Set up an equation

Write an equation using $47 + y = 180$ .

Compute the missing angle

Subtract $47$ from $180$ to find $y$ .

Desmos Guide

Enter the subtraction

In Desmos, type 180-47 and press enter.

Connect it to the diagram

The value shown is the measure of $y$ in degrees because $y$ is supplementary to $47^\circ$ .

Step-by-step Explanation

Use a supplementary-angle relationship

Because the $47^\circ$ angle and $y^\circ$ form a straight line, they are supplementary:

47^\circ + y^\circ = 180^\circ.

Solve for $y$

Subtract $47^\circ$ from both sides:

y = 180 - 47 = 133.

Therefore, $y = 133^\circ$ .

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