Question

Help only need 44 please help

Answer 1

44.

1. Given

2. Vertical angles are congruent

3. angle 1 congruent to angle 5

4. Def congruence

Answer 2

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 variables. 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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