Question

1. find the values of x and y in the diagram.

chapter 5 chapter review 291

Explanation:

Step1: Identify congruent segments

The tick marks show the segment of length $26$ is congruent to $5y+1$, so:
$5y + 1 = 26$

Step2: Solve for y

Subtract 1, then divide by 5:
$5y = 25 \implies y = \frac{25}{5} = 5$

Step3: Identify supplementary angle

The angle $8x^\circ$ forms a linear pair with a right angle, so:
$8x + 90 = 180$

Step4: Solve for x

Subtract 90, then divide by 8:
$8x = 90 \implies x = \frac{90}{8} = 11.25$

Answer:

$x = 11.25$, $y = 5$