Question

geochallenge 3

part 4: exterior angles
use the exterior angle theorem to find the values of \\(\angle abc\\) and \\(\angle cde\\).
given:
\\(\angle cde = 7x + 10\\)
\\(\angle lcb = 10x - 1\\)
\\(\angle dbc = 7x - 4\\)

using the triangle inequality theorem, list the sides of the triangle from smallest to largest.

Explanation:

Set up the exterior angle equation

Using the Exterior Angle Theorem knowledge point

$$
LATEXBLOCK0
$$

Solve for x

Using the Exterior Angle Theorem knowledge point

$$
LATEXBLOCK1
$$

Calculate the required angles

Using the Exterior Angle Theorem and Supplementary Angles knowledge points

$$
LATEXBLOCK2
$$

Order the sides of the second triangle

Using the Angle-Side Relationship and Triangle Inequality Theorem knowledge points

$$
LATEXBLOCK3
$$

Answer:

Question 1

The values of the angles are:

• \(\angle ABC = 173.5^\circ\)
• \(\angle CDE = 20.5^\circ\)

Question 2

The sides of the triangle from smallest to largest are:

• The side opposite the \(46.6^\circ\) angle, then the side opposite the \(56.6^\circ\) angle, and finally the side opposite the \(76.8^\circ\) angle.