Question

directions: use the diagram below to answer questions 1 - 4.

1. name the vertex of each angle.

a. ∠1
b. ∠2

1. name the sides of each angle.

a. ∠7
b. ∠abd

1. write another name for each angle.

a. ∠adb
b. ∠5

1. name an angle with vertex b that appears to be an acute angle.
2. qs bisects ∠pqr. use the diagram and the given angle measure to find the indicated angle measures.

given m∠pqs = 63°. find each angle measure.
a. m∠rqs
b. m∠pqr

Explanation:

Step1: Recall angle - vertex definition

The vertex of an angle is the common endpoint of the rays that form the angle.

Step2: Identify vertex of ∠1

For ∠1, the vertex is point E.

Step3: Identify vertex of ∠2

For ∠2, the vertex is point B.

Step4: Recall angle - side definition

The sides of an angle are the two rays that form the angle.

Step5: Identify sides of ∠7

The sides of ∠7 are rays BA and BC.

Step6: Identify sides of ∠ABD

The sides of ∠ABD are rays BA and BD.

Step7: Recall alternative angle - naming

An angle can be named in different ways.

Step8: Find alternative name for ∠ADB

Another name for ∠ADB is ∠2.

Step9: Find alternative name for ∠5

Another name for ∠5 is ∠EAD.

Step10: Recall acute - angle definition

An acute angle is an angle whose measure is less than 90°.

Step11: Identify acute angle at vertex B

An acute angle with vertex B could be ∠ABD.

Step12: Recall angle - bisector property

If a ray bisects an angle, it divides the angle into two equal - measure angles.

Step13: Find m∠RQS

Since QS bisects ∠PQR and m∠PQS = 63°, then m∠RQS=m∠PQS = 63°.

Step14: Find m∠PQR

Since m∠PQR=m∠PQS + m∠RQS and m∠PQS = m∠RQS = 63°, then m∠PQR=63°+63° = 126°.

Answer:

1.
a. E
b. B
2.
a. Rays BA and BC
b. Rays BA and BD
3.
a. ∠2
b. ∠EAD
4.
a. An example: ∠ABD
5.
a. 63°
b. 126°