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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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wlad13 [49]

The number 7 is the best prediction of the output when the input is 13.

<h3>What is the equation of a line passing through two given points in 2 dimensional plane?</h3>

Suppose the given points are (x_1, y_1) and (x_2, y_2), then the equation of the straight line joining both two points is given by

(y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)

The equation of the line is found as;

\rm y-y_1=  \frac{y_2-y_1}{x_2-x_1}      \\\\ \rm y-9=                                         \frac{31-9}{2+5} (x+5)\\\\ 7y-63 = \frac{31-9}{2+5} (c+5)\\\\ 7y-63=22x+110\\\\ 7y= 22x+173 \\\\ but ,x=13\\\\ 7y=22 \times 13 +173\\\\ y= \frac{1259}{7} \\\\ y= 179

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