Chapter 1.1, Problem 6PSA

a.

To determine

To Find: The all possible name of given angle.

Answer to Problem 6PSA

  $\angle RPO,\angle P$

Explanation of Solution

Given:

  

Concept Used:

Angle is the intersection of two common rays.

Calculation:

The given angle $\angle OPR$ can be named as

  $\angle RPO,\angle P$

Conclusion:

  $\angle RPO,\angle P$

b.

To determine

To Find: The vertex of the angle $\angle TOS$ .

Answer to Problem 6PSA

  $S$

Explanation of Solution

Given:

  

Concept Used:

Angle is the intersection of two common rays having one common vertex.

Calculation:

The vertex of the given angle $\angle TOS$ is $S$ .

Conclusion:

The vertex of the given angle $\angle TOS$ is $S$ .

c.

To determine

To Find: The number of angles formed using the vertex R.

Answer to Problem 6PSA

Three angles formed using the vertex R.

Explanation of Solution

Given:

  

Concept Used:

Angle is the intersection of two common rays having one common vertex.

Calculation:

The angles formed using the vertex R are $\angle SRO,\angle ORP\text{and }\angle SRP$

Thus, three angles formed using the vertex R.

Conclusion:

Three angles formed using the vertex R.

d.

To determine

To Find: The all possible name of given angle.

Answer to Problem 6PSA

  $\angle PST,\angle OST,\angle TSO,\angle O$

Explanation of Solution

Given:

  

Concept Used:

Angle is the intersection of two common rays.

Calculation:

The given angle $\angle TSP$ can be named as

  $\angle PST,\angle OST,\angle TSO,\angle O$

Conclusion:

  $\angle PST,\angle OST,\angle TSO,\angle O$

e.

To determine

To Find: The number of triangles formed in the given figure.

Answer to Problem 6PSA

Eight triangles are in the given figure.

Explanation of Solution

Given:

  

Concept Used:

Triangle is a three sided closed polygon.

Calculation:

The triangles in the given figures are

  $\Delta OPR,\Delta ORS,\Delta OST,\Delta OTP,\Delta PRS,\Delta RST,\Delta STP\text{and }\Delta TPR$

Thus there are eight triangles in the given figure.

Conclusion:

Eight triangles in the given figure.