Question

1. (11x + 4)° 5x° (5y + 5)° (13y - 5)°

Explanation:

Step1: Use property of parallelogram (opposite angles are equal)

Set up equations. For the angles involving \(x\): \(5x=11x + 4\) is incorrect. The correct property for adjacent - angles in a parallelogram is that they are supplementary (\(a + b=180^{\circ}\)). So, \(5x+(11x + 4)=180\).

$$5x+11x+4 = 180$$

$$16x+4=180$$

$$16x=180 - 4$$

$$16x=176$$

$$x = 11$$

Step2: Use property of parallelogram for angles involving \(y\)

For the angles involving \(y\), since adjacent angles in a parallelogram are supplementary, \((5y + 5)+(13y-5)=180\).

$$5y+5 + 13y-5=180$$

$$18y=180$$

$$y = 10$$

Answer:

\(x = 11,y = 10\)