Chapter 2.4, Problem 1PSA

a)

To determine

To Find: $\angle 3$

Answer to Problem 1PSA

  ${49}^{\circ }$

Explanation of Solution

Given information: $\angle 2$ is complementary to $\angle 3$ . $\angle 4={131}^{\circ }$

Formula used: linear pair axiom, properties of intersecting lines and angles formed between the lines.

$\because \angle 2$ and $\angle 3$ are complementary, hence $\angle 2+\angle 3={90}^{\circ }\mathrm{....}(1)$

Also, by hence pair axiom, $\angle 3+\angle 4={180}^{\circ }$ .

Given $\angle 4={131}^{\circ }$ , hence $\angle 3={181}^{\circ }-{131}^{\circ }={49}^{\circ }$

b)

To determine

To Find: $\angle 6$

Answer to Problem 1PSA

  ${131}^{\circ }$

Explanation of Solution

Given information: $\angle 2$ is complementary to $\angle 3$ . $\angle 4={131}^{\circ }$

Formula used: linear pair axiom, properties of intersecting lines and angles formed between the lines.

  $\therefore \angle 6={131}^{\circ }$ (Vertically opposite angles)

c)

To determine

To Find: $\angle 5$

Answer to Problem 1PSA

  ${49}^{\circ }$

Explanation of Solution

Given information: $\angle 2$ is complementary to $\angle 3$ . $\angle 4={131}^{\circ }$

Formula used: linear pair axiom, properties of intersecting lines and angles formed between the lines.

  $\therefore \angle 5={49}^{\circ }$ (Vertically opposite angles)

3rd

  $\angle 2+\angle 3={90}^{\circ }$ (Complementary angles)

d)

To determine

To Find: $\angle 2$

Answer to Problem 1PSA

  ${41}^{\circ }$

Explanation of Solution

Given information: $\angle 2$ is complementary to $\angle 3$ . $\angle 4={131}^{\circ }$

Formula used: linear pair axiom, properties of intersecting lines and angles formed between the lines.

Put $\angle 3={49}^{\circ }$ we get $\angle 2={41}^{\circ }$

e)

To determine

To Find: $\angle 1$

Answer to Problem 1PSA

  ${139}^{\circ }$

Explanation of Solution

Given information: $\angle 2$ is complementary to $\angle 3$ . $\angle 4={131}^{\circ }$

Formula used: linear pair axiom, properties of intersecting lines and angles formed between the lines.

  $\angle 1+\angle 2={180}^{\circ }$ (Linear pair)

  $\therefore \angle 1+{41}^{\circ }={180}^{\circ }$

  $\therefore \angle 1={139}^{\circ }$

f)

To determine

To Find: $\angle 8$

Answer to Problem 1PSA

  ${41}^{\circ }$

Explanation of Solution

Given information: $\angle 2$ is complementary to $\angle 3$ . $\angle 4={131}^{\circ }$

Formula used: linear pair axiom, properties of intersecting lines and angles formed between the lines.

  $\angle 2=\angle 8$ (Vertically opposite angles)

  $\therefore \angle 8={41}^{\circ }$

g)

To determine

To Find: $\angle 7$

Answer to Problem 1PSA

  ${139}^{\circ }$

Explanation of Solution

Given information: $\angle 2$ is complementary to $\angle 3$ . $\angle 4={131}^{\circ }$

Formula used: linear pair axiom, properties of intersecting lines and angles formed between the lines.

  $\angle 7=\angle 1$ (Vertically opposite angle)

  $\therefore \angle 7={139}^{\circ }$