Question
1. Solve \( -5 / 6+7 / 8 \) 2. How many sides will a regular polygon have if the measure of an exterior angle is \( 24^{\circ} \) ?
Ask by Pollard Daniels. in India
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
1. \(-\frac{5}{6} + \frac{7}{8} = \frac{1}{24}\)
2. A regular polygon with exterior angles of \(24^\circ\) has 15 sides.
Solution
1. To solve (-5/6) + (7/8), we first find a common denominator. The least common denominator of 6 and 8 is 24. Rewriting the fractions:
-5/6 = (-5 × 4)/(6 × 4) = -20/24
7/8 = (7 × 3)/(8 × 3) = 21/24
Now, add the fractions:
-20/24 + 21/24 = (21 - 20)/24 = 1/24
So, (-5/6) + (7/8) = 1/24.
2. For a regular polygon, the sum of the exterior angles is always 360°. If each exterior angle measures 24°, then the number of sides (n) is given by:
n = 360° / 24° = 15
Thus, the regular polygon has 15 sides.
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Simplify this solution Mind Expander
To solve \( -\frac{5}{6} + \frac{7}{8} \), first, find a common denominator. The least common multiple of 6 and 8 is 24. Rewrite the fractions: \( -\frac{5}{6} = -\frac{20}{24} \) and \( \frac{7}{8} = \frac{21}{24} \). Then, combine them: \( -\frac{20}{24} + \frac{21}{24} = \frac{1}{24} \). To find the number of sides in a regular polygon with an exterior angle of \( 24^{\circ} \), use the formula for the exterior angle, which is \( \frac{360^{\circ}}{n} = 24^{\circ} \). Solving for \( n \) gives you \( n = \frac{360^{\circ}}{24^{\circ}} = 15 \). So, the polygon has 15 sides!
