During a sports strategy competition, Tara and Emek received a stadium map showing intersecting passing lanes, but several angle labels were missing. One passing lane met a right-angle guide, where a 58° angle left the complementary angle unlabeled. At another intersection, a 124° angle and its neighboring angle formed a straight line. Tara calculated the missing angles as 32° and 56°, then checked that the relationships were correct. With the completed map, their team followed the planned passing routes and executed the winning game plan.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Check whether the two angles add to 90°.
A teammate says the angle complementary to 58° is 42°. Based on the stadium map, which statement is correct?
The teammate is incorrect because the complementary angle is 32°.The teammate is correct because 58° + 42° = 90°.The teammate is incorrect because the complementary angle is 56°.The teammate is incorrect because complementary angles add to 180°.Correct! Since 58° + 32° = 90°, 32° is the complementary angle.
Remember that complementary angles have a total measure of 90°.
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Hint
Supplementary angles add to 180°.
Another passing lane forms a straight line with a 146° angle. What is the measure, in degrees, of its supplementary angle?
Correct! The supplementary angle is 34°.
Subtract the given angle from 180°.
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Hint
Angles on a straight line have a sum of 180°.
Which explanation correctly verifies Tara's calculation that the angle next to 124° is 56°?
124° + 56° = 180°, so the angles are supplementary.124° + 56° = 90°, so the angles are complementary.124° - 56° = 90°, so the calculation is correct.56° is greater than 124°, so the calculation is correct.Correct! The two angles add to 180°, confirming they are supplementary.
Check which relationship applies to angles that form a straight line.
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