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Answer:
A) The angles marked ∠7 and ∠8 are vertical angles.
B) The angles marked with expressions in y are also vertical angles, so those expressions are equal to each other. Stating this in equation form gives an equation that can be solved for y.
C) y = 24; ∠7 = ∠8 = 89°
Explanation:
A) The angles marked ∠7 and ∠8 are vertical angles, comprised of opposite rays and having a common vertex.
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B) The angles marked with expressions in y are also vertical angles. Vertical angles are congruent, so those expressions are equal to each other. Stating this in equation form gives an equation that can be solved for y.
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C) (5y-29)° = (3y+19)°
2y = 48 . . . . . . . . . . . . divide by °, add 29-3y
y = 24 . . . . . . . . . divide by 2
Angles 7 and 8 are supplementary to the angles marked with expressions in y.
∠7 = ∠8 = 180° -(5y -29)° = 209° -5(24)°
∠7 = ∠8 = 89°