Angle C is an inscribed angle of circle P. Angle C measures (-x + 8) degrees and arc AB measures (12x) degrees. Find x
2 answers:
Answer:
<h2>The variable is 8/7.</h2>Step-by-step explanation:
Givens
To solve this problem, we need to use the Inscribed Angle Theorem which states that an angle inscribed in a circle is half of the subtended arc.
Based on this theorem, we have
Replacing each expression
Therefore, the variable is 8/7.
The rule for this is that the measure in degrees of the inscribed angle is half the measure of the arc in degrees. If angle C measures 8-x and arc AB measures 12x, then the formula to solve for x would be
. Simplifying a bit gives us that 8 - x = 6x. Add x to both sides and we have 8 = 7x and x = 8/7.
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Using relations in a right triangle, it is found that the values of x and y are given by: x = 24, y = 46.4, given by option a.
<h3>What are the relations in a right triangle?</h3>The relations in a right triangle are given as follows:
- The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
- The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
- The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
First, we start with the vertical line h that divides y, that is <u>opposite to an angle of 30º, with hypotenuse 34</u>, hence:
sin(30º) = h/34
0.5 = h/34
h = 17.
Then, h is opposite to an angle of 45º, while the hypotenuse is x, hence:
x = 24.
y is divided into two segments.
- The first is the adjacent to the angle of 30º, while the hypotenuse is 34.
- The second is adjacent to the angle of 45º, while the hypotenuse is 24.
Then:
Then, the value of y is given by:
.
More can be learned about relations in a right triangle at brainly.com/question/26396675
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