Chapter 46, Problem 56A

To determine

(a)

To solve the given formula for the value of $\angle A$.

Answer to Problem 56A

The formula that is $\angle A+\angle B+\angle C={180}^{\circ }$ can be solved for $\angle A$ as $\angle A={180}^{\circ }-\left(\angle B+\angle C\right)$.

Explanation of Solution

Given information:

Given that, the measure of angles shown in the figure can be found using the formula.

  $\angle A+\angle B+\angle C={180}^{\circ }$

  

Calculation:

We have been given the formula, $\angle A+\angle B+\angle C={180}^{\circ }$ to determine the measure of angles shown in the figure.

We need to solve the formula for $\angle A$.

The formula states that,

  $\Rightarrow \angle A+\angle B+\angle C={180}^{\circ }$

Subtracting the sum $\angle B+\angle C$ on both sides, we get

  $\Rightarrow \angle A={180}^{\circ }-\left(\angle B+\angle C\right)$

Hence, the formula that is $\angle A+\angle B+\angle C={180}^{\circ }$ can be solved for $\angle A$ as $\angle A={180}^{\circ }-\left(\angle B+\angle C\right)$.

To determine

(b)

To solve the given formula for the value of angle $\angle B$.

Answer to Problem 56A

The formula that is $\angle A+\angle B+\angle C={180}^{\circ }$ can be solved for $\angle B$ as $\angle B={180}^{\circ }-\left(\angle A+\angle C\right)$.

Explanation of Solution

Given information:

Given that, the measure of angles shown in the figure can be found using the formula.

  $\angle A+\angle B+\angle C={180}^{\circ }$

  

Calculation:

We have been given the formula, $\angle A+\angle B+\angle C={180}^{\circ }$ to determine the measure of angles shown in the figure.

We need to solve the formula for $\angle B$.

The formula states that,

  $\Rightarrow \angle A+\angle B+\angle C={180}^{\circ }$

Subtracting the sum $\angle A+\angle C$ on both sides, we get

  $\Rightarrow \angle B={180}^{\circ }-\left(\angle A+\angle C\right)$

Hence, the formula that is $\angle A+\angle B+\angle C={180}^{\circ }$ can be solved for $\angle B$ as $\angle B={180}^{\circ }-\left(\angle A+\angle C\right)$.

To determine

(c)

To solve the formula for $\angle C$.

Answer to Problem 56A

The formula that is $\angle A+\angle B+\angle C={180}^{\circ }$ can be solved for $\angle C$ as $\angle C={180}^{\circ }-\left(\angle A+\angle B\right)$.

Explanation of Solution

Given information:

Given that, the measure of angles shown in the figure can be found using the formula.

  $\angle A+\angle B+\angle C={180}^{\circ }$

  

Calculation:

We have been given the formula, $\angle A+\angle B+\angle C={180}^{\circ }$ to determine the measure of angles shown in the figure.

We need to solve the formula for $\angle C$.

The formula states that,

  $\Rightarrow \angle A+\angle B+\angle C={180}^{\circ }$

Subtracting the sum $\angle A+\angle B$ on both sides, we get

  $\Rightarrow \angle C={180}^{\circ }-\left(\angle A+\angle B\right)$

Hence, the formula that is $\angle A+\angle B+\angle C={180}^{\circ }$ can be solved for $\angle C$ as $\angle C={180}^{\circ }-\left(\angle A+\angle B\right)$.