Question

directions: use the diagram below to answer questions 1 - 4. 1. name the vertex of each angle. a. ∠1 b. ∠2 2. name the sides of each angle. a. ∠7 b. ∠abd 3. write another name for each angle. a. ∠adb b. ∠5 3. name an angle with vertex b that appears to be an acute angle. 4. 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 m∠pqr

Explanation:

Step1: Recall vertex - definition

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

Step2: Identify vertex of ∠1

The vertex of ∠1 is point E.

Step3: Identify vertex of ∠2

The vertex of ∠2 is point B.

Step4: Recall angle - sides 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 BC and BA.

Step6: Identify sides of ∠ABD

The sides of ∠ABD are rays BA and BD.

Step7: Recall angle - naming rules

An angle can be named in different ways.

Step8: Find another name for ∠ADB

Another name for ∠ADB is ∠5.

Step9: Find another name for ∠5

Another name for ∠5 is ∠ADB.

Step10: Recall acute - angle definition

An acute angle is an angle with a measure between 0° and 90°.

Step11: Identify acute angle at B

∠ABD appears to be an acute angle with vertex B.

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° because of the angle - bisector property.

Step14: Find m∠PQR

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

Answer:

1.
a. E
b. B
2.
a. Rays BC and BA
b. Rays BA and BD
3.
a. ∠5
b. ∠ADB
4.
a. 63°
b. 126°