Question

20 pts Examine the diagram. Transversal n intersects lines l and m to form 8 angles. The angles formed with line l, clockwise from top left are 63 degrees, (15 x minus 3) degrees, blank, blank. The angles formed with line m, clockwise from top left are (8 x + 7) degrees, blank, 1, blank. What is the m∠1?
a)21°


b)42°


c)71°


D)82°

Answer 1

Answer:

c.) 71

Step-by-step explanation:

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Answer 2

The measure of angle 1 is 71° ⇒ c

Step-by-step explanation:

Look to the attached figure:

∵ Line l intersect line n

∴ Angle 63° and angle (15x - 3) are linear pair

- The sum of the linear pair angles is 180°

∵ 63° + (15x - 3)° = 180°

- Add like terms

∴ 60 + 15x = 180

- Subtract 60 from both sides

∴ 15x = 120

- Divide both sides by 15

∴ x = 8

∵ Line m intersect line n

∴ Angle (8x + 7) and angle 1 are vertical opposite angles

- The vertical opposite angles are equal in measure

∴ m∠1 = 8x + 7

∵ x = 8

- Substitute the value of x to find m∠1

∴ m∠1 = 8(8) + 7

∴ m∠1 = 64 + 7

∴ m∠1 = 71

The measure of angle 1 is 71°

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