(Algebra 1 ~ High School)
2 answers:
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Using equivalent angles, the solutions are given as follows:
a) .
b) .
c)
Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
For item a, we have to find the equivalent angle on the 2nd quadrant, where the sine is also positive.
Hence:
Hence .
For item b, if two angles are complementary, the sine of one is the cosine of the other.
Complementary angles add to 90º = 0.5pi, hence:
The equivalent angle on the second quadrant is:
Hence the solutions are:
For item c, the angles are also complementary, hence:
The tangent is also positive on the third quadrant, hence the equivalent angle is:
Hence the solutions are:
More can be learned about equivalent angles at brainly.com/question/28163477
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Let's solve for x first.
To find x, use the interior angles on same side of a transversal theorem.
The interior angles on sam side of a transversal are supplemantary angles, and supplementary angles sum up to 180 degrees.
Thus, we have:
(23x - 16) + (8x - 21) = 180
23x - 16 + 8x - 21 = 180
Combine like terms:
23x + 8x - 21 - 16 = 180
31x - 37 = 180
Add 37 to both sides:
31x - 37 + 37 = 180 + 37
31x = 217
Divide both sides by 31:
To find y, use the vertical angles theorem.
Vertical angles are congruent.
Thus we have:
7y - 23 = 23x - 16
Since x = 7, substitute x for 7 in the equation above to find y.
7y - 23 = 23(7) - 16
7y - 23 = 161 - 16
7y - 23 = 145
Add 23 to both sides:
7y - 23 + 23 = 145 + 23
7y = 168
Divide both sides by 7:
x = 7
y = 24
ANSWER:
x = 7
y = 24