Question

Which statement justifies why ∠ABF measures 130°?

Given: angles ABD and DBC are complementary

Point B is on line AE between points A and E, point B is on line FD between points F and D, ray BC intersects with line AE at point B, line FD intersects with line AE at point B, the measure of angle ABD is 50 degrees, and it is given that angles ABD and DBC are complementary.

A linear pair is two adjacent, supplementary angles.
The sum of the measures of complementary angles is 90 degrees.
If two angles are vertical angles, then they are congruent.
Alternate interior angles are congruent.

Answer 1

Answer:

A. A linear pair is two adjacent, supplementary angles.

Step-by-step explanation:

from the description,

< ABD = $50^{o}$, so that;

< ABD + <DBC = $90^{o}$

$50^{o}$ + <DBC =  $90^{o}$

<DBC =  $90^{o}$ -  $50^{o}$

          = $40^{o}$

Thus,

<FBE = < ABD = $50^{o}$ (vertically opposite angles)

<ABF + <FBE = $180^{o}$  (supplementary angles)

<ABF +  $50^{o}$ =  $180^{o}$

<ABF =  $180^{o}$ - $50^{o}$

         = $130^{o}$

The statement that justifies why <ABF measures $130^{o}$ is a linear pair is two adjacent, supplementary angles.

Answer 2

Answer:

its A

Step-by-step explanation: