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- 53.3 ° approxiametly
- In the given question:
- an angle which is three times of its compliment and less than 20°
- based on this statement , the equation formed
- 3x-20° = 180° (
- sum of supplement)
- 3x =180-20
- 3x= 160
- x=53.3
- complement angle is a sum of two angles which is equal to 90° , if two angles add up to form a right angle, then these angles are referred to as complementary angles
- supplement angle is sum of two angles which is equal to 180° , if two angles add up, to form a straight angle, then those angles are referred to as supplementary angles.
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The correct answer is C. All reference angles must be less than 90 degrees.
This is helpful when learning more complex topics including circular trigonometry and the unit circle, because the reference angle (typically denoted as theta prime) has the same trig values (sine and cosine) no matter which quadrant the angle is located in. Additionally, the reference angle is always the smallest angle possible between the terminal side of the angle and the x-axis; therefore, it must always be less than 90 degrees or else another smaller (and thus correct) reference angle could be made in another quadrant.
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Since <em>l</em> and <em>m</em> are parallel, the unlabeled angle adjacent to the 63° one also has measure (7<em>x</em> - 31)° (it's a pair of alternating interior angles).
Then the three angles nearest line <em>m</em> are supplementary so that
(7<em>x</em> - 31)° + 63° + (5<em>x</em> - 8)° = 180°
Solve for <em>x</em> :
(7<em>x</em> - 31) + 63 + (5<em>x</em> - 8) = 180
12<em>x</em> + 24 = 180
12<em>x</em> = 156
<em>x</em> = 13
The bottom-most angle labeled with measure (4<em>y</em> + 27)° is supplementary to the angle directly adjacent to it, so this unlabeled angle has measure 180° - (4<em>y</em> + 27)° = (153 - 4<em>y</em>)°. The interior angles of any triangle have measures that sum to 180°, so we have
(7<em>x</em> - 31)° + 63° + (153 - 4<em>y</em>)° = 180°
We know that <em>x</em> = 13, so 7<em>x</em> - 31 = 60. Then this simplifies to
123° + (153 - 4<em>y</em>)° = 180°
Solve for <em>y</em> :
123 + (153 - 4<em>y</em>) = 180
276 - 4<em>y</em> = 180
96 = 4<em>y</em>
<em>y</em> = 24
