Question

a. name the vertex of <4 b. Name the sides of <1 c. Write another Name for <5 d. classify each angle

Answer 1

Answer:

A. vertex B

B. Side BC and BD

C. Angle EBD

Step-by-step explanation:

Answer 2

An angle is an undefined term in plane geometry.

• The vertex of $\angle 4$ is B
• The sides of $\angle 1$ are BC and BD
• Another name for $\angle 5$ is $\angle DBE$.
• $\angle FBC$ is a right angle
• $\angle EBF$ is an obtuse angle
• $\angle ABC$ is a straight angle.
• $\angle EBC = 144$
• $\angle ABE =13.5$

Vertex of $\angle 4$

The vertex of an angle is the point where the rays that form the angle meet.

From the diagram, rays BE and BA meet at point B to form $\angle 4$.

Hence, the name of the vertex is B

Sides of $\angle 1$

The sides of an angle are the rays or sides that form the angle

$\angle 1$ is formed by rays BC and BD

Hence, the sides are BC and BD

Another name for $\angle 5$

An angle can be named by combining the sides and the vertex.

The sides of $\angle 5$ are DB and BE, while the vertex is B

This means that rays DB and BE meet at point B

Hence, another name is $\angle DBE$

Classify the angles

Angles are classified based on the measure

$\angle FBC$ is a right angle, because $\angle FBC = 90^o$

$\angle EBF$ is an obtuse angle because $\angle EBF$ is greater than $90^o$ but less than $180^o$

$\angle ABC$ is a straight angle, because $\angle ABC= 180^o$

Angle bisector

The line or ray that divides an angle into equal halves is an angle bisector.

Ray BE is an angle bisector, because it divides $\angle DBA$ into two equal halves.

Find $\angle EBC$

We have:

$\angle EBD = 36$

$\angle DBC = 108$

$\angle EBC$ is calculated using:

$\angle EBC = \angle EBD +\angle DBC$

$\angle EBC = 108+36$

$\angle EBC = 144$

Find $\angle ABE$

We have:

$\angle EBF = 117$

$\angle DBC = 108$

$\angle ABE$ is calculated using:

$\angle EBF = \angle ABE +\angle EBD + \angle ABF$

Where

$\angle ABF = 90$

$\angle ABE = \angle EBD$

So, we have:

$117 = \angle ABE +\angle ABE + \angle 90$

$117 = 2\angle ABE + 90$

Collect like terms

$2\angle ABE =117 - 90$

$2\angle ABE =27$

Divide both sides by 2

$\angle ABE =13.5$

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