Lines x and y are parallel. If B=3x 16 , G=2x 29 , and A=2y 17 then find the values of x and y. The figure is not drawn to scale.Two parallel lines x and y connected by a transversal line cutting them both. 8 angles form as a result and are labeled A-H(10 points)
Since lines x and y are parallel, the corresponding angles formed by the transversal will be congruent.
Let's examine the angles formed by this transversal:
A and E are corresponding angles, so they are congruent.
B and F are alternate interior angles, so they are congruent.
C and G are consecutive interior angles, so they are supplementary (they add up to 180°).
D and H are alternate interior angles, so they are congruent.
We're given the measures of angles B, G, and A, so we can set up equations using this information.
From angle B, we have: B = 3x + 16
From angle G, we have: G = 2x + 29
From angle A, we have: A = 2y + 17
Now let's use these equations to solve for x and y.
Since B and F are congruent, we know that B + F = 180°.
Substituting the expressions for B and F, we have: (3x + 16) + (2x + 29) = 180
Combining like terms, we get: 5x + 45 = 180
Subtracting 45 from both sides, we have: 5x = 135
Dividing both sides by 5, we get: x = 27
Now that we have the value of x, we can substitute it into the equations for B and G to find their values:
B = 3x + 16 = 3(27) + 16 = 81 + 16 = 97
G = 2x + 29 = 2(27) + 29 = 54 + 29 = 83
So, the value of x is 27, B = 97, and G = 83.
Let's move on to solving for y.
Since C and G are supplementary, we know that C + G = 180°.
Substituting the expressions for C and G, we have: (2y + 17) + (2x + 29) = 180
Substituting the values of x and G, we have: (2y + 17) + 83 = 180
Combining like terms, we get: 2y + 100 = 180
Subtracting 100 from both sides, we have: 2y = 80
Dividing both sides by 2, we get: y = 40
Therefore, the value of y is 40.