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need the answer now The figure shows adjacent angles BAC and CAD.

Adjacent angles BAC and CAD sharing common ray AC

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. (6 points)

Part B: Find the m∠BAC. Show all your work. (4 points)

Sagot :

mhanifa

Answer:

  • A) x = 25,
  • B) m∠BAC = 49°

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Given

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

Solution

Part A

BAD is the sum of adjacent angles BAC and CAD according to angle addition postulate:

  • 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

Find the m∠BAC:

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

Cathenna

Answer:

A. Value of x = 25°

B. m∠BAC = 49°

Step-by-step explanation:

According to the question,

Adjacent angles BAC and CAD share common ready AC. By this statement we can conclude that sum of angles BAC & CAD will be equal to angle BAD.

It's given that,

m∠BAD = 129°

m∠BAC = (2x −1)°

m∠CAD = (3x + 5)°

A. So, by using angle addition postulate we get,

[tex] \rm \implies \angle BAC + \angle CAD = \angle BAD \\ \\ \rm \implies (2x - 1) \degree + (3x + 5) \degree = 129 \degree \\ \\ \rm \implies 5x + 4\degree = 129 \degree \\ \\ \rm \implies 5x = 129 \degree - 4\degree \\ \\ \rm \implies 5x = 125 \degree \\ \\ \rm \implies x = \frac{125}{5} \degree \\ \\ \rm \implies x = 25 \degree[/tex]

B. By substituting value of x we get,

[tex] \rm \implies m \angle BAC = (2x −1) \degree \\ \\ \rm \implies m \angle BAC = (2 \times 25 −1) \degree \\ \\ \rm \implies m \angle BAC = (50 −1) \degree \\ \\ \rm \implies m \angle BAC = 49\degree[/tex]

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