What is the value for x?

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x =

image shows isosceles triangle a b c with angle c and side a b congruent to side c b. angle measure measures 69 degrees. angle b measures 5 x plus 2 degrees. angle c measures 9 y minus 3 degrees.

x = 8

Step-by-step explanation:

From the diagram above, since  the triangle is an isosceles triangle and side  AB is congruent to side CB, then angle A must be equal to angle B.

angle A = angle C

    69°     =  9y - 3

To get the value of y, we add 3 to both-side of the equation and then divide both-side of the equation by 9

69 + 3 =  9y -3 + 3

72     =   9y

Divide both-side of the equation by 9

72/9  =   9y/9

8  =  y

y =8

But what we are looking for is x;

69°  +   (9y -3)°  +  (5x + 2)°  =  180 °  ( sum of angle in a triangle)

To get the value of x, we will substitute y=8  in the equation above and then simplify

69  +  9(8) - 3 +  5x  + 2 = 180

69 + 72 - 3  + 5x  + 2 = 180

138 +  5x + 2 = 180

140 + 5x   = 180

subtract both-side of the equation by 140

140 - 140 + 5x  = 180 -140

5x  =  40

Divide both-side of the equation by 5

5x/5  =  40/5

x  =  8

Therefore the value of x is 8

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