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In this practice problem, we explore supplementary and complementary angles to find missing angle measures. Given that angles <PQR and <RQS are supplementary, we derive the value of angle y. The problem also includes vertical angles <PQR and <TQS, allowing us to determine the value of x. Furthermore, using complementary angles <ABD and <DBC, we solve for z. This exercise aids in understanding angle relationships and enhances problem-solving skills in geometry.
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125° x° A D z 15° B C Find the missing angle measures. <PQR and <RQS are supplementary angles, so mPQR+ mRQS= 180° 125 + y = 180 -125 -125 y = 55° P R Q y° T S <PQR and <TQS are vertical angles. So, the value of x is 125°. <ABD and <DBC are complementary angles, so mABD+ mDBC= 90° z + 15 = 90 -15 -15 z = 75° Bell Work