Use the figure shown to complete each of the following questions. Angle NTS is a straight angle.
1.
∠QTR and ______ are complementary.
• ∠QTS
• ∠RTS
• ∠PTN
• ∠QT
1. ∠QTR and RTS are complementary.
2. ∠QTN and QTS are supplementary.
3. If ∠PTQ measures 29°, then PTN measures 61.
4. If ∠NTR measures 148°, then ∠RTS measures 32.
5. ∠PTN is adjacent to PTS.
These are the answers
∠QTS and ∠RTS are complementary angles. Complementary angles add up to 90 degrees. In the figure, ∠QTS and ∠RTS are two of the angles formed by two lines that intersect at point T. Because angle NTS is a straight angle, the lines intersecting at point T form a right angle. Therefore, ∠QTS and ∠RTS are complementary angles.
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To determine which angle is complementary to ∠QTR, we need to understand what complementary angles are. Complementary angles are two angles that add up to 90 degrees.
In the figure provided, angle NTS is a straight angle, which means it measures 180 degrees. Therefore, we can subtract the measure of ∠QTR from 180 degrees to find the measure of the complementary angle.
Given that ∠QTR is a right angle (90 degrees), we can subtract 90 from 180: 180 - 90 = 90 degrees.
From the given options, the angle that measures 90 degrees is ∠RTS. Therefore, the correct answer is ∠RTS.