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Nina [5.8K]
3 years ago
12

Suppose that circles A and B have a central angle measuring 75°. Additionally, circle A has a radius of 5 2 feet and the radius

of circle B is 9 2 feet. If the length of the intercepted arc for circle A is 25 24 π feet, what is the length of the intercepted arc for circle B? A) 5 8 π feet B) 8 5 π feet C) 8 15 π feet D) 15 8 π feet
Mathematics
1 answer:
spin [16.1K]3 years ago
6 0
Let 
rA--------> radius of the circle A
rB-------> radius of the circle B
LA------> the length of the intercepted arc for circle A
LB------> the length of the intercepted arc for circle B
 
we have that
rA=5/2 ft
rB=9/2 ft
rA/rB=5/9--------> rB/rA=9/5
LA=(25/24)π ft
 we know that
if Both circle A and circle B have a central angle , the ratio of the radius of circle A to the radius of circle B is equals to the ratio of the length of circle A to the length of circle B
rA/rB=LA/LB--------> LB=LA*rB/rA-----> [(25/24)π*9/5]----> 15/8π ft
 
the answer is
the length of the intercepted arc for circle B is 15/8π ft
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Lelechka [254]

B is the correct answer. 3(x+1)=24

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3 years ago
In need of geometry help, once again my stupid brain cant remember anything.
melomori [17]

You cannot rely on the drawing alone to prove or disprove congruences. Instead, pull out the info about the sides and angles being congruent so we can make our decision.

The diagram shows that:

  • Side AB = Side XY (sides with one tick mark)
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  • Angle C = Angle Z (similar angle markers)

We have two pairs of congruent sides, and we also have a pair of congruent angles. We can't use SAS because the angles are not between the congruent sides. Instead we have SSA which is not a valid congruence theorem (recall that ambiguity is possible for SSA). The triangles may be congruent, or they may not be, we would need more information.

---------------

So to answer the question if they are congruent, I would say "not enough info". If you must go with a yes/no answer, then I would say "no, they are not congruent" simply because we cannot say they are congruent. Again we would need more information.

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Answer:

m∠5 = 44°; m∠7 = 44°

Step-by-step explanation:

Angle 4 and 1 are supplementary (they make up a line) and their sum is equal to 180 degrees.

Subtracting the measure of angle 4 from 180 degrees gives the measure of angle 1. (180 - 136 = 44).

So Angle 1's measure is 44 degrees.

According to the Corresponding Angle Postulate, Angle 1 and Angle 5 are congruent. Therefore, m∠5 = 44°

According to the Vertical Angles Postulate (if two angles are vertical, they are congruent), ∠5 ≅ ∠7, meaning that m∠5 = m∠7.

So m∠7 = 44°

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