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The figure shows adjacent angles BAC and CAD.
Given:
m∠BAD = 129°
m∠BAC = (2x −1)°
m∠CAD = (3x + 5)°

Part A: Using the angle addition postulate, write and solve an equation for x. Show all your work.

Part B: Find the m∠BAC. Show all your work.

Sagot :

Mhanifaidn

Answer:

  • A) x = 25,
  • B) m∠BAC = 49°.

-----------------------------------

Given:

  • m∠BAD = 129°,
  • m∠BAC = (2x −1)°,
  • m∠CAD = (3x + 5)°,
  • BAC and CAD are adjacent.

Part A

Angle addition postulate gives us:

  • m∠BAD = m∠BAC + m∠CAD

Substitute and solve for x:

  • 129 = 2x - 1 + 3x + 5
  • 129 = 5x + 4
  • 125 = 5x
  • x = 125/5
  • x = 25

Part B

Substitute the value of x and find the m∠BAC:

  • m∠BAC = 2*25° - 1° = 50° - 1° = 49°
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