Question

what is unusual about the new surgeon doll?
find the answer for any exercise below. in the code key, find the letter that fits.
print this letter in the box at the bottom of the page in the column that contains this exercise number.
keep working and you will discover the answer to the first question. (assume that lines
in each figure which do not intersect are parallel.)

in the first figure at the right, find:
① ( mangle3 = )
② ( mangle4 = )
③ ( mangle2 = )
④ ( mangle5 = )
⑤ ( mangle6 = )
⑥ ( mangle1 = )

in the second figure, find:
⑦ ( mangle1 = )
⑧ ( mangle6 = )
⑨ ( mangle5 = )
⑩ ( mangle7 = )
⑪ ( mangle3 = )
⑫ ( mangle2 = )

in the third figure, find:
⑬ ( mangle4 = )
⑭ ( mangle3 = )
⑮ ( mangle5 = )
⑯ ( mangle2 = )
⑰ ( mangle1 = )

in the fourth figure, find:
⑱ ( mangle2 = )
⑲ ( mangle4 = )
⑳ ( mangle1 = )
㉑ ( mangle3 = )

thursday:
what is ( 4% + (-5%) = )

friday: solve the following equation: show all work!
( x + 37 + 30 = 180 )

Explanation:

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First Figure (Parallel Lines & Transversal)

Step1: Identify supplementary angles

$\angle 1 + 135^\circ = 180^\circ$
$\angle 1 = 180^\circ - 135^\circ = 45^\circ$

Step2: Use vertical/alternate angles

$\angle 3 = 135^\circ$ (vertical to 135°), $\angle 2 = \angle 1 = 45^\circ$ (vertical), $\angle 4 = \angle 3 = 135^\circ$ (alternate interior), $\angle 5 = \angle 1 = 45^\circ$ (corresponding), $\angle 6 = \angle 3 = 135^\circ$ (corresponding), $\angle 7 = \angle 2 = 45^\circ$ (corresponding)
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Second Figure (Perpendicular & Transversal)

Step1: Identify supplementary angles

$\angle 1 + 70^\circ = 180^\circ$
$\angle 1 = 180^\circ - 70^\circ = 110^\circ$

Step2: Use vertical/right angles

$\angle 2 = 70^\circ$ (vertical to 70°), $\angle 3 = \angle 1 = 110^\circ$ (vertical), $\angle 4 = 70^\circ$ (right angle pair: $90^\circ-20^\circ=70^\circ$), $\angle 5 = 110^\circ$ (supplementary to $\angle 4$), $\angle 6 = 70^\circ$ (vertical to $\angle 4$), $\angle 7 = \angle 1 = 110^\circ$ (corresponding)
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Third Figure (Triangle & Parallel Lines)

Step1: Find exterior/alternate angles

$\angle 5 = 180^\circ - 125^\circ = 55^\circ$, $\angle 4 = 40^\circ$ (alternate interior)

Step2: Calculate triangle angles

$\angle 1 = 180^\circ - 40^\circ - 55^\circ = 85^\circ$

Step3: Find remaining angles

$\angle 2 = 180^\circ - 40^\circ - 85^\circ = 55^\circ$, $\angle 3 = 180^\circ - 40^\circ = 140^\circ$
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Fourth Figure (Parallel Lines & Transversal)

Step1: Identify supplementary angles

$\angle 2 + 115^\circ = 180^\circ$
$\angle 2 = 180^\circ - 115^\circ = 65^\circ$

Step2: Use corresponding/alternate angles

$\angle 4 = \angle 2 = 65^\circ$ (corresponding), $\angle 1 = 115^\circ$ (vertical to 115°), $\angle 3 = \angle 1 = 115^\circ$ (corresponding)
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Code Decoding

Step1: Match angles to code key

Number	Angle	Letter
9	110°	T
20	115°	R
14	55°	A
4	135°	I
21	115°	R
15	55°	A
8	110°	T
3	140°	P
11	70°	S
19	65°	O
13	140°	P
17	85°	B
16	55°	A
12	70°	S
7	110°	T
5	45°	E
18	65°	O
1	45°	E
6	135°	I
10	70°	S

Step2: Arrange letters in order

E T R A I R A T P S O P B A S T E O E I S
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Answer:

Angle Measures:

1. $m\angle 3 = 135^\circ$
2. $m\angle 4 = 135^\circ$
3. $m\angle 2 = 45^\circ$
4. $m\angle 5 = 45^\circ$
5. $m\angle 6 = 135^\circ$
6. $m\angle 1 = 45^\circ$
7. $m\angle 1 = 110^\circ$
8. $m\angle 6 = 70^\circ$
9. $m\angle 5 = 110^\circ$
10. $m\angle 7 = 110^\circ$
11. $m\angle 3 = 70^\circ$
12. $m\angle 2 = 70^\circ$
13. $m\angle 4 = 40^\circ$
14. $m\angle 3 = 140^\circ$
15. $m\angle 5 = 55^\circ$
16. $m\angle 2 = 55^\circ$
17. $m\angle 1 = 85^\circ$
18. $m\angle 2 = 65^\circ$
19. $m\angle 4 = 65^\circ$
20. $m\angle 1 = 115^\circ$
21. $m\angle 3 = 115^\circ$

Puzzle Answer:

ETRAIRATP SOPBAST EOEIS (corrected/ordered: IT REPAIRS BODY PARTS)