m∠6 is (2x - 5) ° and m∠8 is (x + 5) °. Parallel lines q and s are cut by transversal r. On line q where it intersects with line r, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line s where it intersects with line r, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7. What is m∠3? °

Question

Mathematics

Guillermo

10 August, 05:58

m∠6 is (2x - 5) ° and m∠8 is (x + 5) °. Parallel lines q and s are cut by transversal r. On line q where it intersects with line r, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line s where it intersects with line r, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7. What is m∠3? °

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Answers (1)

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Diana Chavez · Answer 1

115 degrees = m∠3

Step-by-step explanation:

Set angles 6 and 8 equal to 180 degrees because they are supplementary angles.

2x - 5 + x + 5 = 180 Combine like terms

3x = 180 Divide both sides by 3

x = 60

m∠8 ≅ m∠3 because they are vertical angles

Plug x into the equation for angle 8

60 + 5

65 degrees

Subtract this from 180 to find the measure of angle 3.

180 - 65 = 115