Question

question 8 of 10 which of the following statements must be true about this diagram? check all that apply. a. the degree measure of ∠3 equals the sum of the degree measures of ∠1 and ∠2. b. m∠4 is greater than m∠1. c. the degree measure of ∠4 equals the sum of the degree measures of ∠2 and ∠3. d. the degree measure of ∠4 equals the sum of the degree measures of ∠1 and ∠2. e. m∠3 is greater than m∠2 f. m∠4 is greater than m∠2.

Explanation:

Step1: Recall exterior - angle theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.

Step2: Analyze ∠3

∠3 is an exterior angle of the triangle. The non - adjacent interior angles to ∠3 are ∠1 and ∠2. So, \(m\angle3=m\angle1 + m\angle2\). Also, since \(m\angle3=m\angle1 + m\angle2\), then \(m\angle3>m\angle2\).

Step3: Analyze ∠4

∠4 is a straight - angle adjacent to ∠3. \(m\angle4 = 180^{\circ}\) and \(m\angle3+m\angle4 = 180^{\circ}\). Also, \(m\angle4>m\angle1\) and \(m\angle4>m\angle2\) because \(m\angle4\) is a straight - angle and \(m\angle1\) and \(m\angle2\) are interior angles of a non - degenerate triangle.

Answer:

A. The degree measure of ∠3 equals the sum of the degree measures of ∠1 and ∠2.
B. \(m\angle4\) is greater than \(m\angle1\).
E. \(m\angle3\) is greater than \(m\angle2\).
F. \(m\angle4\) is greater than \(m\angle2\).