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

✔️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.

Explanation:

Vertical angles are formed when two straight lines intersect each other at a certain point. The diagram given is a typical example. This, vertical opposite angles formed are said to be congruent, that is their measures are equal to each other.

The following statements are true of the given diagram:

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

(<CBA and ,<DBE are vertically opposite angles)

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

(They are both vertically opposite angles)

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

(<CBA and <CBD are supplementary angles)