Find the value of x in the triangle where one angle is (8x - 23)° and another angle is 34°.
Understand the Problem
The question is asking to find the value of x in a triangle where one angle is expressed as (8x - 23)° and another as 34°. The sum of the angles in a triangle adds up to 180°, so we will need to use that property to solve for x.
Answer
$x = 21.125$
Answer for screen readers
The value of $x$ is $21.125$.
Steps to Solve
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Recognizing angle relationships The angles in a triangle sum up to 180°. We have one angle as $(8x - 23)°$ and another as $34°$. Let the third angle be represented as $y°$.
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Setting up the equation We can express the equation for the sum of the angles: $$ (8x - 23) + 34 + y = 180 $$
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Finding the third angle Since the problem does not provide the third angle, we can express $y$ in terms of the other angles, but first let's simplify the equation using $34°$: $$ 8x - 23 + 34 = 180 $$
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Simplifying the equation Combine the known angles: $$ 8x + 11 = 180 $$
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Isolating x Now, subtract 11 from both sides: $$ 8x = 180 - 11 $$
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Solving for x Calculate the right side: $$ 8x = 169 $$
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Dividing by the coefficient of x Divide both sides by 8: $$ x = \frac{169}{8} $$
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Final calculation Evaluate: $$ x = 21.125 $$
The value of $x$ is $21.125$.
More Information
The angles of a triangle always add up to 180°, which is a fundamental property used to solve various problems involving triangles. The calculations showed how to isolate the variable to find the value of $x$.
Tips
- Forgetting that the sum of all angles in a triangle is 180°.
- Miscalculating the addition and subtraction of constants when simplifying the equation.
- Failing to divide properly when isolating the variable.
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