1) 72 + 18 =90. Therefore the angles are complementary angles
2) Angles one and two are a pair of opposite angles made by two intersecting lines. Those are called vertical angles.
3) Those two are right angles, and two right angles add up to 180. So they are right angles and supplementary angles.
4) Adjacent angles
5) Vertical angles and supplementary (because both are right angles)
6) Right angles, supplementary, linear, adjacent angles.
7) Complementary and adjacent angles.
8) Angle of a straight line is 180. So 180-21 should equal x. x=159
9) As stated in number 2, vertical angles are congruent. x=129
10) 38 and x are complementary angles. (it shows a box on the angle formed by both of them, which means it is a right angle.) 90-38 = 52
11) Vertical angle rule. y = 93. The sum of 93, y, x, and z is 360, because the degree of a full circle is 360 degrees. so, 360-93-93 is 174. However, because of the vertical angle rule we will know that x=z. so 174/2 is 87.
x=87 and z=87
12) If you read the question, it states m∠PQR is 147, and ∠PQR is consisted of 119 and x. So, 147-119 is x. x=28
13) W and 34 are linear angles. Linear angles add up to 180 degrees. So, 180-34. w=146. Angle x is labeled with a box at the vertex of the angle. That indicates it is a right angle. x=90. The angle formed with 34 and z is labeled with a box at the vertex, indicating 34+z is 90. Therefore, 90-34=z. z=56. Finally, because angle x is linear with angle (y+z), we will know that y+z is equal to 90. Therefore, y+z=90, y+56=90, y=90-56, y=34
14) We are given that m∠AEC is 41. ∠AEC and ∠AED are linear angles. So, m∠AED = 180-41. m∠AEC=139
15) ∠DEF is a right angle, indicated by the box label at the vertex. ∠DEF and ∠CEF are linear angles, therefore m∠CEF = 180-90. m∠CEF=90
16) ∠DEB and ∠AEC are vertical angles. Therefore m∠AEC and m∠DEB are equal. ∠DEB=41
17) ∠DEB and ∠BEF form a right angle together. In question 16 we confirmed that m∠DEB is 41. Therefore m∠BEF is equal to 90-41.
m∠BEF=49
18) In question 15 we confirmed that m∠CEF is 90, and in question 17 we confirmed that m∠BEF is 49. So m∠CEB must be 90+49. m∠CEB=139
19) In question 15 we confirmed that m∠CEF is 90, and the direction states m∠AEC is 41. Therefore m∠AEF is 90+41. m∠AEF=131
20) Vertical angles are congruent. Therefore ∠PQR is the same degree measure as ∠SQT. m∠PQR=109
21) Complementary angles add up to 90. Therefore ∠2+∠3 = 90. And it is given that ∠2=24. Therefore ∠3 = 90-24. ∠3=66
22) Supplementary angles add up to 180. Therefore ∠K+∠L= 180. And it is given that ∠K=56. Therefore ∠L = 180-56. ∠L=124
