Question

Identify at least two pairs of congruent angles in the figure and explain how youknow they are congruent.b.What is the measure of angle CBE? Explain how you knowName a triangle congruent to triangle CBE. Explain how you know.

Answer 1

Angle CBE has a measure of 50 degrees. Triangle ABC is congruent to triangle CBE.

Step-by-step explanation:

In the given figure, we can identify two pairs of congruent angles: angle ABC and angle CDE, and angle BAC and angle DEC. This is because they have the same measure of 50 degrees, as shown in the figure.

To calculate the measure of angle CBE, we can use the fact that the sum of all angles in a triangle is 180 degrees. Since we know that angle ABC and angle BAC both have a measure of 50 degrees, we can subtract their sum from 180 degrees to find the measure of angle CBE.

180 degrees - (50 degrees + 50 degrees) = 80 degrees. Therefore, angle CBE has a measure of 80 degrees.

Now, to determine a triangle congruent to triangle CBE, we can use the Side-Angle-Side (SAS) congruence criteria. This states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

In this case, triangle ABC has the same side lengths as triangle CBE (side AB and side BC are equal to side CB and side BE, respectively) and the included angle of both triangles is angle ABC, which we already know is congruent to angle CBE. Therefore, triangle ABC is congruent to triangle CBE.

In conclusion, angle CBE has a measure of 50 degrees and triangle ABC is congruent to triangle CBE. This can be verified by using the SAS congruence criteria and the fact that the sum of all angles in a triangle is 180 degrees.

Answer 2

A)

FCE and CAB are congruent angles they are formed by the same line FA and two parallel lines between them

FEC and EDB are congruent angles for the same reason

B)we will write the measure of each angle based on the statement

The line AD contains the angles ABC,CBE and EBD if we sum all angles we make the line and the measure of a line is 180 degrees so

`\begin{gathered} \text{ABC}+\text{CBE}+\text{EBD}=180 \\ 63+\text{CBE}+45=180 \\ \text{CBE}=180-63-45 \\ \text{CBE}=72 \end{gathered}`

the CBE is 72°

C)

congruent triangles are those that have all their angles equal,Since all the triangles are copies of triangle ABC, they are all congruent since they all measure the same but are located in different ways

so a triangle congruent to triangle CBE can be any for example :ABC,BED or FCE