Question

1. what is the value of x? see example 3

for exercises 21–23, find each value of x for the given value of y. round to the nearest tenth.
see examples 4 and 5

1. y = 16
2. y = 20
3. y = 18

Explanation:

Problem 20

Step1: Apply proportional segments theorem

When three parallel lines cut two transversals, the segments are proportional: $\frac{16}{x} = \frac{x}{4}$

Step2: Cross-multiply to solve for $x$

$x^2 = 16 \times 4$
$x^2 = 64$

Step3: Take positive square root

$x = \sqrt{64}$

Step1: Apply Angle Bisector Theorem

The angle bisector divides the opposite side proportionally: $\frac{AD}{DB} = \frac{AC}{CB}$
$\frac{7}{x} = \frac{15}{16}$

Step2: Cross-multiply to solve for $x$

$15x = 7 \times 16$
$15x = 112$

Step3: Calculate $x$ and round

$x = \frac{112}{15} \approx 7.5$

Step1: Apply Angle Bisector Theorem

$\frac{7}{x} = \frac{15}{20}$

Step2: Cross-multiply to solve for $x$

$15x = 7 \times 20$
$15x = 140$

Step3: Calculate $x$ and round

$x = \frac{140}{15} \approx 9.3$

Answer:

$8$

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Problem 21 ($y=16$)