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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)



Answer :

The values of x and m∠BAC are 25° and 49° respectively

What is the angle addition postulate?

The angle addition postulate is a theorem stating that  two or more angles side by side that they share a common vertex and arm, then the sum of those angles will be equal to the total sum of the resulting angle.

Then, we can say that;

m∠BAC  + m∠CAD = m∠BAD

Given that;

  • m∠BAD = 129°
  • m∠BAC = (2x −1)°
  • m∠CAD = (3x + 5)°

Substitute the values

2x - 1 + 3x + 5 = 129

collect like terms

2x + 3x = 129 - 4

5x = 125

Make 'x' the subject

x = 125/ 5

x = 25°

But, m∠BAC = (2x −1)° = 2(25) - 1 = 50 - 1 = 49°

Thus, the values of x and m∠BAC are 25° and 49° respectively

Learn more about angle addition postulate here:

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