Question

Given the image below and that ZABD and ZDBC form a linear pair, what is the

measure of angle ABD?
Show ALL work to receive credit.
(1) write your equation for the angle addition postulate (2pt)
(2) plug in the information given into your equation (1pt)
(3) solve for x (1pt)
(4) solve for angle ABD (1pt)
5x
D
3x+4

Answer 1

Answer: m∠ABD = 2x - 4

Explanation:

To find the measure of angle ABD, we can follow these steps:

1. Write the equation for the angle addition postulate:

According to the angle addition postulate, the sum of the measures of two adjacent angles is equal to the measure of the larger angle. In this case, angle ABD and angle ZDBC are adjacent angles, so we can write the equation: m∠ABD + m∠ZDBC = m∠ZABD

2. Plug in the given information into the equation:

From the image, we know that angle ZABD measures 5x degrees, and angle ZDBC measures 3x + 4 degrees. So we can substitute these values into the equation: m∠ABD + (3x + 4) = 5x

3. Solve for x:

Simplify the equation by combining like terms: m∠ABD + 3x + 4 = 5x

Subtract 3x from both sides: m∠ABD + 4 = 2x

Subtract 4 from both sides: m∠ABD = 2x - 4

4. Solve for angle ABD:

We now have the measure of angle ABD in terms of x: m∠ABD = 2x - 4

By following these steps, we have determined that the measure of angle ABD is given by the equation m∠ABD = 2x - 4.

I hope this helps :)