For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?(1 point)
Responses
6°6 degrees
53°
53 degrees
29°29 degrees
15.3°15.3 degrees
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To find the measure of each angle, we can set the measures of the angles equal to each other.
So, 5x + 23 = 3x + 35
Subtracting 3x from both sides gives us:
2x + 23 = 35
Subtracting 23 from both sides gives us:
2x = 12
Dividing both sides by 2 gives us:
x = 6
Now we can substitute this value of x back into either equation to find the measure of the angles.
Using the equation m∠2 = 5x + 23, we find:
m∠2 = (5 × 6) + 23
= 30 + 23
= 53 degrees
So, m∠2 = 53 degrees.
And since the angles are vertical angles, m∠4 will also measure 53 degrees.
Therefore, the measure of each angle is 53 degrees.