41. Name a pair of vertical angles:
Vertical angles are angles directly opposite of each other. In this case, your answer choices can be (but not limited too): ∠1 & ∠4.
42. Name a pair of complementary angles:
Complementary angles are angles that = 90° when combined. In this case, you need a pair, and so you need 2 angles that = 90°, not one. Your answer choice can NOT BE: ∠3 & ∠6. Your answer choices CAN BE: ∠1 & ∠2, ∠4 & ∠5.
43. Name a pair of supplementary angles.
Supplementary angles = 180° The only pair of angles is ∠3 & ∠6, which when added, = 180° (90 + 90 = 180). Remember that it is only a pair, and so cannot be more than 2 angles.
44. Given: ∠1 ≅ ∠2
1. ∠1 ≅ ∠2 Reason: Given
2. ∠2 ≅ ∠5 Reason: Definition of Vertical Angles
3. ∠1 ≅ ∠5 Reason: Transitive Property of Angle Congruence
Another reason can be CPCTC*
4. m∠1 = m∠5 Reason: CPCTC
45. If m∠1 = 60°, then m∠3 + m∠ 5 = ________________.
m∠3 = 90° (Definition of Vertical angles), since the direct opposite angle of ∠3 is ∠6, which has the measurement of 90°.
m∠1 = 60° (Given)
This means by definition of vertical angles, m∠4 = 60°
By the definition of supplementary angles, m∠6 + (m∠5 + m∠4) = 180°
m∠6 = 90° (given). Plug in the corresponding numbers to the corresponding variables:
90 + m∠5 + m∠4 = 180
Isolate the 2 <em>variables</em>. Note the equal sign, what you do to one side, you do to the other. Subtract 90 from both sides.
90 (-90) + m∠5 + m∠4 = 180 (-90)
m∠5 + m∠4 = 180 - 90
m∠5 + m∠4 = 90
Note that it is given to us that m∠1 = 60°. This means that by definition of vertical angles, m∠4 = 60° as well. Plug in 60 for m∠4, and solve:
m∠5 + m∠4 = 90
m∠5 + 60 = 90
Isolate the variable. Subtract 60 from both sides:
m∠5 + 60 (-60) = 90 (-60)
m∠5 = 90 - 60
m∠5 = 30.
m∠5 + m∠3 = 30 + 90 = 120°
120° is your answer.
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