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Gekata [30.6K]
3 years ago
13

If the measure of angle ABF=6x+26 and the measure of angle EBF=2x9 and measure of angle ABE= 11x-31 find the measure of angle AB

F

Mathematics
1 answer:
Hunter-Best [27]3 years ago
4 0

Its not clearly given that whether EBF = 2x + 9 or 2x - 9.

I have written the solution for both.

If EBF = 2x + 9,

then ABF = 6x + 26 and ABE = 11x - 31.

Now, ABE = ABF + EBF

11x - 31 = (6x + 26) + (2x + 9)

           = (6x + 2x) + (26 + 9)

           = 8x + 35

11x - 8x = 35 + 31

3x = 66

x = 22

Therefore, ABF = 6x + 26 = 6(22) + 26 = 132 + 26 = 158°

If EBF = 2x - 9,

then ABF = 6x + 26 and ABE = 11x - 31.

Now, ABE = ABF + EBF

11x - 31 = (6x + 26) + (2x - 9)

           = (6x + 2x) + (26 - 9)

           = 8x + 17

11x - 8x = 17 + 31

3x = 48

x = 16

Therefore, ABF = 6x + 26 = 6(16) + 26 = 96 + 26 = 122°

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On a coordinate plane, triangle A B C is shown. Point A is at (negative 1, 6), point B is at (negative 1, 1), and point C is at
attashe74 [19]

Answer:

<u> 10 +√10</u>

Step-by-step explanation:

Given the coordinates of the triangle expressed as

A(-1,6), B(-1, 1) and C(2,2)

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Since AB = AC

P = AC + BC + AC

P = 2AC + BC

get the length AC using the formula;

Given A(-1,6) and C(2,2)

AC = √(2-(-1))²+(2-6)

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B(-1, 1) and C(2,2)

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BC = √3²+1²

BC = √9+1

BC = √10

Perimeter = 2(5)+√10

Perimeter = 10 + √10

Hence the perimeter of the triangle is<u> 10 +√10</u>

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