Question

use the value of \\(x\\) from the previous question to determine the angle measurements.

press a hotspot, then type your response, and press submit. repeat for each response.

\\(m\angle abd = \underline{\quad}^{\circ}\\)
\\(m\angle abc = \underline{\quad}^{\circ}\\)

\\((3x + 5)^{\circ}\\)
\\((x + 15)^{\circ}\\)

Explanation:

Set up the linear pair equation

The angles \(\angle ABD\) and \(\angle ABC\) form a linear pair along the straight line \(DC\).
By the Linear Pair Postulate, their measures sum to \(180^\circ\):

$$(3x + 5) + (x + 15) = 180$$

Solve for x

Combine like terms and solve the linear equation:

$$4x + 20 = 180$$

$$4x = 160$$

$$x = 40$$

Calculate the measure of angle ABD

Substitute \(x = 40\) into the expression for \(m\angle ABD\):

$$m\angle ABD = 3(40) + 5 = 120 + 5 = 125^\circ$$

Calculate the measure of angle ABC

Substitute \(x = 40\) into the expression for \(m\angle ABC\):

$$m\angle ABC = 40 + 15 = 55^\circ$$

Verify the sum of the angles

Check that the sum of the calculated angles equals \(180^\circ\):

$$125^\circ + 55^\circ = 180^\circ$$

The calculations are correct.

Answer:

Use the value of x from the previous question to determine the angle measurements.

\(m\angle ABD =\) <blank>125</blank>\(^\circ\)

\(m\angle ABC =\) <blank>55</blank>\(^\circ\)