Question

Lines LaTeX: CEC E and LaTeX: ADA D intersect at LaTeX: BB. Lines C E and A D intersect at the point B. Angle A B C is labeled 37 degrees. Select all the true statements. Group of answer choices The measure of angle LaTeX: CBA C B A is equal to the measure of angle LaTeX: DBE D B E . The sum of the measures of angles LaTeX: CBA C B A and LaTeX: DBE D B E is 180 degrees. The measure of angle LaTeX: CBD C B D is equal to the measure of angle LaTeX: ABE A B E . The sum of the measures of angles LaTeX: CBD C B D and LaTeX: CBA C B A is 180 degrees. The sum of the measures of angles LaTeX: CBA C B A and LaTeX: DBE D B E is 90 degrees.

Answer 1

*see attachment below for the figure referred to

Answer:

*The measure of angle <CBA is equal to the measure of angle <DBE.

*The measure of angle CBD is equal to the measure of angle ABE.

*The sum of the measures of angles CBD and CBA is 180 degrees.

Step-by-step explanation:

Since lines CE and AD bisects at D, they form two pairs of vertical angles that are congruent to each other. The vertical angle pairs formed are:

<CBD and <ABE;

<CBA and <DBE

Thus:

m<CBD = m<ABE;

m<CBA = <DBE = 37°

Also, m<CBA + m<CBD = 180° (supplementary linear pair)

m<ABE + m<DBE = 180° (supplementary linear pair)

Therefore, the following statements are TRUE:

*The measure of angle <CBA is equal to the measure of angle <DBE.

*The measure of angle CBD is equal to the measure of angle ABE.

*The sum of the measures of angles CBD and CBA is 180 degrees.