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Elan Coil [88]
3 years ago
6

What is x? I have been having trouble with these

Mathematics
1 answer:
Wittaler [7]3 years ago
3 0

Answer:

x=4

Step-by-step explanation:

(whole secant) x (external part) =   (whole secant) x (external part)

(6+x) * 6 =(5+x+3) *5

(6+x) * 6 =(x+8) *5

Distribute

36+6x = 5x+40

Subtract 5x from each side

36+6x-5x = 5x-5x+40

36+x = 40

Subtract 36 from each side

36+x-36 = 40-36

x = 4

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Question 1

The angles 52 degrees match up. So if the sides are in proportion, then the triangles are similar.

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Question 2

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We have a pair of congruent 54 degree angles shown. There's another pair of angles at the very top that overlap (aka shared angles).

Since we have two pairs of congruent angles, <u>the two triangles are similar</u>.

This time we use the <u>AA Similarity theorem</u>

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Question 4

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Repeat for the middle-most sides

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We get the same linear scale factor 1.5 each time. Therefore, <u>the triangles are similar</u> due to the <u>SSS Similarity theorem</u>

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Question 5

Any angle is equal to itself due to the <u>reflexive property</u>. So that will go for reason number 2.

Reason 3 is <u>SAS similarity</u> because we have the sides in proportion (statement 1) and the angles are congruent (statement 2).

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