Question

5
w=____
x=____
y=____
z=____
6
w=____
x=____
y=____
z=____
complementary / supplementary angles! vertical angles #3 g...... 2007

Explanation:

For Problem ⑤

Step1: Set up supplementary angle equation

$5x + x = 180$

Step2: Solve for $x$

$6x = 180 \implies x = \frac{180}{6} = 30$

Step3: Find $w$ (vertical to $5x$)

$w = 5x = 5\times30 = 150$

Step4: Find $y$ (vertical to $x$)

$y = x = 30$

Step5: Find $z$ (vertical to $w$)

$z = w = 150$

Step1: Set up complementary angle equation

$x + (x+20) = 90$

Step2: Solve for $x$

$2x + 20 = 90 \implies 2x = 70 \implies x = 35$

Step3: Find $w$ (vertical to $x+20$)

$w = x+20 = 35+20 = 55$

Step4: Find $y$ (supplementary to $x$)

$y = 180 - x = 180-35 = 145$

Step5: Find $z$ (vertical to $x$)

$z = x = 35$

Answer:

$w=150$, $x=30$, $y=30$, $z=150$

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For Problem ⑥