Question

1. there is a diagram with intersecting lines. one angle is 49°, another is (7x - 23)°, another is (3x)°, and another is (11y - 1)°. lines l and m are also shown.

Explanation:

Step1: Set up equation for vertical angles

$7x - 23 = 3x$

Step2: Solve for $x$

Subtract $3x$ from both sides: $4x - 23 = 0$
Add 23 to both sides: $4x = 23$
Divide by 4: $x = \frac{23}{4} = 5.75$

Step3: Find angle measure for $3x$

$3x = 3 \times 5.75 = 17.25^\circ$

Step4: Set up equation for supplementary angles

$17.25 + 49 + (11y - 1) = 180$

Step5: Simplify and solve for $y$

Combine constants: $65.25 + 11y = 180$
Subtract 65.25: $11y = 114.75$
Divide by 11: $y = \frac{114.75}{11} = \frac{459}{44} \approx 10.43$

Answer:

$x = 5.75$, $y \approx 10.43$ (or $x = \frac{23}{4}$, $y = \frac{459}{44}$)