QuestionIf $\angle A$ is supplementary to $\angle B$ and $\angle B=115^{\circ}$ , find $\angle A$ .

Studdy Solution

STEP 1

Assumptions1. $\angle A$ is supplementary to $\angle B$ . $\angle B=115^{\circ}$
3. Two angles are supplementary if the sum of their measures is $180^{\circ}$

STEP 2

We can express the relationship between $\angle A$ and $\angle B$ using the definition of supplementary angles. $\angle A + \angle B =180^{\circ}$

STEP 3

Now, plug in the given value for $\angle B$ to solve for $\angle A$ .
$\angle A +115^{\circ} =180^{\circ}$

STEP 4

Rearrange the equation to isolate $\angle A$ .
$\angle A =180^{\circ} -115^{\circ}$

STEP 5

Calculate the measure of $\angle A$ .
$\angle A =180^{\circ} -115^{\circ} =65^{\circ}$ So, $\angle A =65^{\circ}$ .

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QuestionIf $\angle A$ is supplementary to $\angle B$ and $\angle B=115^{\circ}$ , find $\angle A$ .

Studdy Solution

STEP 1

Assumptions1. $\angle A$ is supplementary to $\angle B$ . $\angle B=115^{\circ}$
3. Two angles are supplementary if the sum of their measures is $180^{\circ}$

STEP 2

We can express the relationship between $\angle A$ and $\angle B$ using the definition of supplementary angles. $\angle A + \angle B =180^{\circ}$

STEP 3

Now, plug in the given value for $\angle B$ to solve for $\angle A$ .
$\angle A +115^{\circ} =180^{\circ}$

STEP 4

Rearrange the equation to isolate $\angle A$ .
$\angle A =180^{\circ} -115^{\circ}$

STEP 5

Calculate the measure of $\angle A$ .
$\angle A =180^{\circ} -115^{\circ} =65^{\circ}$ So, $\angle A =65^{\circ}$ .

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QuestionIf ∠A\angle A∠A is supplementary to ∠B\angle B∠B and ∠B=115∘\angle B=115^{\circ}∠B=115∘, find ∠A\angle A∠A.

Studdy Solution

STEP 1

Assumptions1. ∠A\angle A∠A is supplementary to ∠B\angle B∠B . ∠B=115∘\angle B=115^{\circ}∠B=115∘3. Two angles are supplementary if the sum of their measures is 180∘180^{\circ}180∘

STEP 2

We can express the relationship between ∠A\angle A∠A and ∠B\angle B∠B using the definition of supplementary angles.∠A+∠B=180∘\angle A + \angle B =180^{\circ}∠A+∠B=180∘

STEP 3

Now, plug in the given value for ∠B\angle B∠B to solve for ∠A\angle A∠A.∠A+115∘=180∘\angle A +115^{\circ} =180^{\circ}∠A+115∘=180∘

STEP 4

Rearrange the equation to isolate ∠A\angle A∠A.∠A=180∘−115∘\angle A =180^{\circ} -115^{\circ}∠A=180∘−115∘

STEP 5

Calculate the measure of ∠A\angle A∠A.∠A=180∘−115∘=65∘\angle A =180^{\circ} -115^{\circ} =65^{\circ}∠A=180∘−115∘=65∘So, ∠A=65∘\angle A =65^{\circ}∠A=65∘.

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QuestionIf $\angle A$ is supplementary to $\angle B$ and $\angle B=115^{\circ}$ , find $\angle A$ .

Assumptions1. $\angle A$ is supplementary to $\angle B$ . $\angle B=115^{\circ}$
3. Two angles are supplementary if the sum of their measures is $180^{\circ}$

We can express the relationship between $\angle A$ and $\angle B$ using the definition of supplementary angles. $\angle A + \angle B =180^{\circ}$

Now, plug in the given value for $\angle B$ to solve for $\angle A$ .
$\angle A +115^{\circ} =180^{\circ}$

Rearrange the equation to isolate $\angle A$ .
$\angle A =180^{\circ} -115^{\circ}$

Calculate the measure of $\angle A$ .
$\angle A =180^{\circ} -115^{\circ} =65^{\circ}$ So, $\angle A =65^{\circ}$ .