While exploring an abandoned mountain bridge after a landslide, Emek and Tara discovered that several steel support beams had shifted. The repair guide showed one angle at an intersection measured 68°, but the other angles were missing. Using vertical angles and supplementary angle relationships, they determined that the opposite angle was also 68° and the two adjacent angles were 112°. They repeated the same reasoning at other beam intersections to identify which supports were correctly aligned and which required adjustment. After the repairs matched the geometric relationships, engineers reopened the bridge, allowing travelers to cross the mountain safely once again.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Vertical angles formed by two intersecting lines have equal measures.
At one beam intersection, an angle measures 68°. What is the measure of the vertical angle opposite it?
90°112°68°180°Correct! The vertical angle also measures 68°.
Remember that opposite angles at an intersection are equal.
Next🎉 Congrats! You got this question!
Hint
Adjacent angles formed by intersecting lines are supplementary.
At another beam intersection, one angle measures 74°. What is the measure, in degrees, of either adjacent angle?
Correct! Each adjacent angle measures 106°.
Subtract 74° from 180°.
Next🎉 Congrats! You got this question!
Hint
Opposite angles must match, and each adjacent pair must add to 180°.
Which set of angle measures could occur at one intersection of two straight support beams?
68°, 90°, 68°, 134°68°, 68°, 112°, 112°68°, 122°, 68°, 102°68°, 112°, 68°, 112°Correct! Opposite angles are equal, and adjacent angles sum to 180°.
Check both conditions: equal vertical angles and supplementary adjacent angles.
Next🎉🎉🎉🎉🎉🎉🎉🎉
🎉 Congrats! You finished this challenge set!
