Question

select all the true statements. the sum of the measures of angles cba and dbe is 90 degrees. the measure of angle cba is equal to the measure of angle dbe. the sum of the measures of angles dbc and cba is 180 degrees. the sum of the measures of angles cba and dbe is 180 degrees.

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. Angle CBA and angle DBE are vertical angles.

Step2: Recall linear - pair property

Angles DBC and CBA form a linear - pair. The sum of angles in a linear - pair is 180 degrees.

Step3: Analyze each statement

• For the sum of angles CBA and DBE: Since they are vertical angles, they are equal, and their sum is not 180 degrees.
• For the sum of angles DBC and CBA: They form a linear - pair, so $\angle DBC+\angle CBA = 180^{\circ}$.
• For the measure of angle CBA and DBE: As vertical angles, $\angle CBA=\angle DBE$.
• For the sum of angles CBA and DBE: They are not complementary (sum is not 90 degrees) as they are vertical angles.

Answer:

The sum of the measures of angles DBC and CBA is 180 degrees. The measure of angle CBA is equal to the measure of angle DBE.