Question

1. three lines intersect as shown in the diagram. which of the following statements about this diagram are true? select all that apply. a. the measure of angle h equals the sum of the measures of angles c and i. b. the measure of angle d equals the sum of the measures of angles b and c. c. the measure of angle j equals the sum of the measures of angles c and e. d. the measure of angle g equals the sum of the measures of angles e and i. e. the measure of angle b equals the sum of the measures of angles c and l.

Explanation:

Step1: Recall exterior - angle property

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

Step2: Analyze option A

For angle H, consider the triangle formed by the lines. Angle H is an exterior angle of a triangle with non - adjacent interior angles C and I. So, by the exterior - angle property, \(m\angle H=m\angle C + m\angle I\).

Step3: Analyze option B

For angle D, consider the relevant triangle. Angle D is an exterior angle of a triangle where the non - adjacent interior angles are B and C. So, \(m\angle D=m\angle B + m\angle C\).

Step4: Analyze option C

For angle J, consider the triangle. Angle J is an exterior angle of a triangle with non - adjacent interior angles C and E. So, \(m\angle J=m\angle C + m\angle E\).

Step5: Analyze option D

For angle G, consider the triangle. Angle G is an exterior angle of a triangle with non - adjacent interior angles E and I. So, \(m\angle G=m\angle E + m\angle I\).

Step6: Analyze option E

Angle B is not an exterior angle of a triangle with non - adjacent interior angles C and L. So, \(m\angle B
eq m\angle C + m\angle L\).

Answer:

A. The measure of angle H equals the sum of the measures of angles C and I.
B. The measure of angle D equals the sum of the measures of angles B and C.
C. The measure of angle J equals the sum of the measures of angles C and E.
D. The measure of angle G equals the sum of the measures of angles E and I.