# The angles of triangle ABC are in the ratio of 8:3:4. What is the measure of the smallest angle?

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Jim G. Share
Feb 9, 2018

${36}^{\circ}$

#### Explanation:

$\text{sum the parts of the ratio}$

$\Rightarrow 8 + 3 + 4 = 15 \text{ parts}$

$\text{consider the sum of the 3 angles in 15 parts}$

$\text{so "180^@/15=12^@larrcolor(blue)"1 part}$

$\Rightarrow \text{8 parts } = 8 \times 12 = {96}^{\circ}$

$\Rightarrow \text{3 parts } = 3 \times 12 = {36}^{\circ}$

$\Rightarrow \text{4 parts } = 4 \times 12 = {48}^{\circ}$

$\Rightarrow \text{smallest angle } = {36}^{\circ}$

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The text passage contains a single mathematical question about finding the measure of the smallest angle in a triangle given the ratio of its angles. The answer to this question is provided in the explanation section.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# The angles of triangle ABC are in the ratio of 8:3:4. What is the measure of the smallest angle?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

1
Jim G. Share
Feb 9, 2018

${36}^{\circ}$

#### Explanation:

$\text{sum the parts of the ratio}$

$\Rightarrow 8 + 3 + 4 = 15 \text{ parts}$

$\text{consider the sum of the 3 angles in 15 parts}$

$\text{so "180^@/15=12^@larrcolor(blue)"1 part}$

$\Rightarrow \text{8 parts } = 8 \times 12 = {96}^{\circ}$

$\Rightarrow \text{3 parts } = 3 \times 12 = {36}^{\circ}$

$\Rightarrow \text{4 parts } = 4 \times 12 = {48}^{\circ}$

$\Rightarrow \text{smallest angle } = {36}^{\circ}$

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The text passage contains a single mathematical question about finding the measure of the smallest angle in a triangle given the ratio of its angles. The answer to this question is provided in the explanation section.

TYPE: SINGLE_QUESTION_WITH_ANSWER