Question

two vertical angles have measures of $3x$ and $x+50$. the $x=$
select one:
a. 25
b. 10
c. 50
d. 32.5

the measures of the exterior angles of a pentagon are in a ratio of 1:2:3:4:5. the measure of the largest exterior angle is
select one:
a. 48
b. 24
c. 72
d. 120

Explanation:

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First Question:

Step1: Set angles equal (vertical angles)

$3x = x + 50$

Step2: Isolate x (subtract x)

$3x - x = 50$
$2x = 50$

Step3: Solve for x (divide by 2)

$x = \frac{50}{2} = 25$

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Second Question:

Step1: Sum of exterior angles is 360°

Let angles be $1x, 2x, 3x, 4x, 5x$.
$x + 2x + 3x + 4x + 5x = 360$

Step2: Simplify the equation

$15x = 360$

Step3: Solve for x

$x = \frac{360}{15} = 24$

Step4: Find largest exterior angle

$5x = 5 \times 24 = 120$

Answer:

1. a. 25
2. d. 120