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The value of x must be 25.0. The correct option is the second option- 25.0
<h3>Solving Linear equations </h3>From the question, we are to determine the value of x
From the given diagram, we can write that
m ∠SOR + m ∠UOR + m ∠TOU = 180° (<em>Sum of angles on a straight line</em>)
∴ (2x +8)° + (3x - 14)° + (3x -14)° = 180°
2x° + 8° + 3x° -14° + 3x° -14° = 180°
Collect like terms
2x° + 3x° + 3x° + 8° - 14° -14° = 180°
8x° -20° = 180°
8x° = 180° + 20°
8x° = 200°
x = 200/8
x = 25.0
Hence, the value of x must be 25.0. The correct option is the second option- 25.0
Learn more Solving linear equations here: brainly.com/question/1413277
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You can use the identity to write the equation as
Now, from the fundamental equation of trigonometry, deduce an expression for in terms of
:
The equation becomes
Simplify the left hand side and move all terms to left hand side:
Now, if you let , this equation becomes a quadratic equation:
The two solutions of this equations are
We must be careful, because we have to remember that was actually
. This means that
can only assume values between -1 and 1. The second solution exceeds 1, so we reject it. So, we have