Chapter 1.2, Problem 6PSA

a.

To determine

To find: How large is $\angle RPO$ .

Answer to Problem 6PSA

  $\angle RPO=30°$

Explanation of Solution

Given:

  

A rectangle PRST having diagonals PS and TR intersecting at O, with each angle at the corner is of measure 90 degrees. Also $\angle TPO=60°$

Concept Used:

Angles formed at the corner are complementary angle.

Calculation:

A rectangle PRST having diagonals PS and TR intersecting at O, with each angle at the corner is of measure 90 degrees.

  

Also $\angle TPO=60°$

Since, angles formed at the corner are complementary angle.

  $\begin{array}{l}\Rightarrow \angle RPO=90°-\angle TPO\\ \Rightarrow \angle RPO=90°-60°\\ \Rightarrow \angle RPO=30°\end{array}$

Conclusion:

  $\angle RPO=30°$

b.

To determine

To find: How large is $\angle STO$ .

Answer to Problem 6PSA

  $\angle STO=20°$

Explanation of Solution

Given:

  

A rectangle PRST having diagonals PS and TR intersecting at O, with each angle at the corner is of measure 90 degrees. Also $\angle PTO=70°$

Concept Used:

Angles formed at the corner are complementary angle.

Calculation:

A rectangle PRST having diagonals PS and TR intersecting at O, with each angle at the corner is of measure 90 degrees.

  

Also $\angle PTO=70°$

Since, angles formed at the corner are complementary angle.

  $\begin{array}{l}\Rightarrow \angle STO=90°-\angle PTO\\ \Rightarrow \angle STO=90°-70°\\ \Rightarrow \angle STO=20°\end{array}$

Conclusion:

  $\angle STO=20°$

c.

To determine

To find: How large is $\angle POR$ .

Answer to Problem 6PSA

  $\angle POR=130°$

Explanation of Solution

Given:

  

A rectangle PRST having diagonals PS and TR intersecting at O, with each angle at the corner is of measure 90 degrees. Also $\angle TOP=50°$

Concept Used:

Sum of linear pair of angles is 180 degrees.

Calculation:

A rectangle PRST having diagonals PS and TR intersecting at O, with each angle at the corner is of measure 90 degrees.

  

Also $\angle TOP=50°$

Sum of linear pair of angles is 180 degrees.

  $\begin{array}{l}\Rightarrow \angle POR=180°-\angle TOP\\ \Rightarrow \angle POR=180°-50°\\ \Rightarrow \angle POR=130°\end{array}$

Conclusion:

  $\angle POR=130°$

d.

To determine

To find: The nature of $\angle TOS$ .

Answer to Problem 6PSA

  $\angle TOS$ is obtuse angle.

Explanation of Solution

Given:

  

A rectangle PRST having diagonals PS and TR intersecting at O, with each angle at the corner is of measure 90 degrees.

Concept Used:

Sum of angles of triangle is 180 degrees. Also alternate interior angles are equal in measure. Vertically opposite angles are equal in measure.

Calculation:

A rectangle PRST having diagonals PS and TR intersecting at O, with each angle at the corner is of measure 90 degrees.

  

As we have $\angle POR=130°$

Since, vertically opposite angles are equal in measure.

  $\begin{array}{l}\Rightarrow \angle TOS=\angle POR\\ \Rightarrow \angle TOS=130°\end{array}$

Thus, $\angle TOS$ is an obtuse angle.

Conclusion:

  $\angle TOS$ is an obtuse angle.