Question

Given: m∠bad = 134° m∠bac = (2x 3)° m∠cad = (4x −1)°

part a: using the angle addition postulate, write and solve an equation for x. show all your work.

Answer 1

By using the angle addition postulate and substituting given values of ∠BAC and ∠CAD into the equation (2x + 3)° + (4x - 1)° = 134°, we find the solution x = 22.

Step-by-step explanation:

The student is asked to use the angle addition postulate to find the value of x in the context of a geometry problem. According to the given information, the angle measure of ∠BAD is 134°, while the measures of ∠BAC and ∠CAD are expressed in terms of x, specifically (2x + 3)° and (4x - 1)°, respectively.

To find x, we use the angle addition postulate, which states that if point A lies inside ∠BAD, then m∠BAC + m∠CAD = m∠BAD. By substituting the given expressions, we can set up the equation: (2x + 3) + (4x - 1) = 134. Combining like terms, we get 6x + 2 = 134. Solving for x, we subtract 2 from both sides to get 6x = 132, and then divide by 6 to find x = 22.

Answer 2

To solve for x using the Angle Addition Postulate, we set up the equation 134° = (2x + 3)° + (4x - 1)°, combine like terms, and solve for x, resulting in x = 22°.

Step-by-step explanation:

The student is asked to apply the Angle Addition Postulate to solve for the variable x. Given m∠bad = 134°, m∠bac = (2x + 3)°, and m∠cad = (4x - 1)°, we can set up the equation:

134° = (2x + 3)° + (4x - 1)°

Solving for x by combining like terms:

134° = 6x + 2°

132° = 6x

x = 22°

By solving this equation, we find that the value of x is 22 degrees. This is how the Angle Addition Postulate is used to solve for a variable when given the measure of an angle and its parts. The key steps are setting up the equation based on the given information, simplifying the equation, and solving for the variable.