Question

mark all congruent angles. solve for x and y
(7y - 20)° (5x - 38)°
(3x - 4)°
3·24 - 29 = 72 - 29 = 43
y = 43 - 17
y = 26
y = 13/4 = 3.25

Explanation:

Step1: Use angle - congruence property

Assume the two angles $(5x - 38)^{\circ}$ and $(3x - 4)^{\circ}$ are congruent (alternate - interior angles if $l\parallel m$). Set up the equation $5x-38 = 3x - 4$.

Step2: Solve the equation for x

Subtract $3x$ from both sides: $5x-3x-38=3x - 3x-4$, which simplifies to $2x-38=-4$. Then add 38 to both sides: $2x-38 + 38=-4 + 38$, so $2x=34$. Divide both sides by 2: $x = 17$.

Step3: Use another angle - relationship

Assume the angle $(7y - 20)^{\circ}$ is related to the found - angle situation. If we assume some angle - congruence (not specified clearly in the problem setup, but if we assume it is equal to one of the other angles in a valid geometric relationship). Let's assume for simplicity that it is equal to the angle $(3x - 4)^{\circ}$ when $x = 17$, so $(3x - 4)^{\circ}=(3\times17 - 4)^{\circ}=47^{\circ}$. Then set up the equation $7y-20 = 47$.

Step4: Solve the equation for y

Add 20 to both sides: $7y-20 + 20=47 + 20$, so $7y=67$. Divide both sides by 7: $y=\frac{67}{7}\approx9.57$.

Answer:

$x = 17$, $y=\frac{67}{7}$