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NikAS [45]
3 years ago
14

A triangle has angles measuring 25 degrees and 45 degrees. What is the measure of the triangle's third angle

Mathematics
1 answer:
katrin [286]3 years ago
8 0

Answer:

110°

Step-by-step explanation:

Let the third angle be x. All the angles in a triangle add up to 180°. From the previous statement, we can write the equation:

25° + 45° + x = 180°

70° + x = 180°

x = 110°

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Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 3 inches, and the larger gear has a ra
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Circumference of a circle is C = 2πr.

part 1)

so the radius of the smaller gear is 3 inches, so after a full rotation, namely a revolution, the smaller gear has covered an arc of 2π(3), or 6π.

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\bf \textit{arc's length}\\\\
s=r\theta ~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad radians\\
------\\
s=6\pi \\
r=7
\end{cases}\implies 6\pi =7\theta \implies \cfrac{6\pi }{7}=\theta



part 2)

since the larger gear has a radius of 7, in a revolution it will have an arc of 2π(7), or 14π.

now, we know the smaller gear does a 6π arc in a revolution, how many revolutions will it do in an arc of 14π?

\bf \begin{array}{ccll}
arc&revolution\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
6\pi &1\\
14\pi &x
\end{array}\implies \cfrac{6\pi }{14\pi }=\cfrac{1}{x}\implies \cfrac{3}{7}=\cfrac{1}{x}\implies x=\cfrac{7}{3}
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