Question

The figures AABC and EDF are shown below.

A
D (24-3.8) in
x
27in
(3x+2)
C
F (2x-4)
A) What is the measure of angle ABC?
A. 3x + 2
B. 2x - 4
C. 24 - 3.8
D. 27

B) What is the length of DE in inches?
A. 3x + 2
B. 2x - 4
C. 24 - 3.8
D. 27

Answer 1

To find the measure of angle ABC, subtract the measures of angle A and angle C from 180 degrees. To find the length of DE, use a proportion with the corresponding sides of the similar triangles AABC and EDF.

Step-by-step explanation:

To find the measure of angle ABC, we can use the fact that the angles in a triangle add up to 180 degrees. Since angle ABC is part of triangle AABC, we can subtract the measures of angle A and angle C from 180 degrees to find the measure of angle ABC.

Therefore, the measure of angle ABC is 180 - (3x + 2) - (2x - 4).

To find the length of DE, we can use the fact that corresponding sides of similar triangles are proportional. Since triangles AABC and EDF are similar, we can set up a proportion with the corresponding sides.

The proportion would be: AB/DE = AC/DF.

We know that AB = 27 inches and AC = 24 - 3.8 inches. We also know that DF = 2x - 4 inches. By substituting these values into the proportion, we can solve for DE.