Inside an old ranger station, Emek and Tara discovered faded blueprints for a historic mountain bridge. Several angle measurements at the intersections of the structural beams had disappeared over time. One drawing showed a 74° angle where two beams crossed, while another adjacent angle was missing. Using the facts that vertical angles are equal and adjacent angles on a straight line are supplementary, they calculated the remaining angles as 74° and 106°. Repeating this reasoning throughout the blueprint, they reconstructed the original engineering layout and revealed how the bridge had been designed to support heavy loads.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Think about the relationship between angles directly across from each other.
At the beam intersection on the blueprint, which relationship explains why the angle opposite the 74° angle also measures 74°?
Adjacent angles are equal.Vertical angles are equal.Supplementary angles are always equal.All angles formed by intersecting lines measure 74°.
Correct! Opposite angles formed by intersecting lines are vertical angles and have equal measures.
Check the rule for angles located directly opposite each other at an intersection.
Next
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Hint
The two adjacent angles are supplementary, so their measures add to 180°.
At another beam intersection on the blueprint, an adjacent pair of angles is labeled 3x° and 2x°. Because the angles form a straight line, what is the value of x?
Correct! The value of x is 36.
Add 3x and 2x, set the sum equal to 180, and solve.
Next
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Hint
Check both the vertical-angle and supplementary-angle relationships.
Tara labels the four angles around one beam intersection in clockwise order as 74°, 106°, 74°, and 106°. Which statement best confirms that her labels are correct?
Opposite angles are equal, and each adjacent pair adds to 180°.All four angles are equal.Each adjacent pair adds to 90°.Only the two 106° angles need to be equal.
Correct! The opposite angles match, and every adjacent pair forms a straight angle.
Verify both conditions that apply when two straight lines intersect.
Next
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Kayıp Köprünün Planları
TR
ARC_G09_GM_01_STORY_02
Kayıp Köprünün Planları
Blueprints of the Lost Bridge
EN
ARC_G09_GM_01_STORY_02
Blueprints of the Lost Bridge