The gear is one of the oldest mechanical devices. It has been used since ancient times for its ability to increase or decrease rotational velocity. When one gear turns another, the outer portions of the gears are turning at the same linear speed. However, when one gear is smaller or larger than the other, the speed of rotation will be different for each gear. Let’s look at an application of gears that you’ve seen before. On a bicycle, the pedals are attached to a large gear at the center of the bike, and a chain connects the large gear to a small gear attached to the rear wheel. The chain does not change the speed of rotation; it serves only to separate the centers of rotation.

Consider a bicycle where the large central gear has a radius of 4 inches and the small back gear has a radius of 2 inches.

part a-How many inches would a point on the outer edge of the large gear travel in a 150º rotation?

part b- What degree of rotation will the small gear undergo when a point on its outer edge travels the same linear distance determined in part A?

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.