October 26th, 2016, 03:24 AM  #1 
Newbie Joined: Oct 2016 From: PSR B162026 b Posts: 2 Thanks: 0  Proving angle Relationships help
Could anyone please help me with these questions? Last edited by skipjack; November 9th, 2016 at 05:39 AM. 
November 9th, 2016, 06:38 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 16,194 Thanks: 1147 
The answers below may not be word perfect. I've done the arithmetic for you, but haven't named every theorem used. Some results may follow from definitions rather than theorems. A "straight angle" is (measures) 180°. 1. The two angles combine to form a straight angle, and you are told the second is 57°, so the first is 123°. Not sure of the best theorem to cite here  possibly the straight angles theorem. 2. The right angle shown is 90°, so the same principle as that used in (1) tells you that angle 6 is 180°  90°  22° = 68°. 3. By the vertical angle theorem, the numbered angles are equal, so each measures 38°. 4. 4x + 11 + 3x + 1 = 180, so 7x = 168, which implies x = 24. Hence angles 13 and 14 are respectively 107° and 73°. 5. By definition, two angles are complementary if their sum is 90°. As for (2), angle 9 = angle 7 = 180°  90°  41° = 49°. Angle 10 = 180°  49°  41°  49° = 41°. 6. By the vertical angle theorem, 4x  26 = 3x + 4, so x = 30. Hence angle 2 and angle 3 are each 94°. 7. a. $\small\angle$QPS $\cong$ $\small\angle$TPR  given b. Congruent angles have equal measure by definition. c. Angle addition d. m$\small\angle$QPR + m$\small\angle$RPS $\ \ \ $ m$\small\angle$TPS + m$\small\angle$RPS e. m$\small\angle$QPR = m$\small\angle$TPS  subtraction property f. $\small\angle$QPR $\cong$ $\small\angle$TPS  definition of conguent angles 

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