Question
or two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?
Answers
GPT 3.5
Vertical angles are always congruent, meaning they have the same measure. So, we can set the two angle measures equal to each other and solve for x.
m∠1 = m∠3
(2x+26)° = (3x+32)°
Simplifying the equation:
2x + 26 = 3x + 32
Subtracting 2x from both sides:
26 = x + 32
Subtracting 32 from both sides:
-6 = x
Now that we know the value of x, we can substitute it back into either angle measure to find the actual measure of each angle, let's use m∠1:
m∠1 = (2x+26)°
m∠1 = (2(-6)+26)°
m∠1 = (-12+26)°
m∠1 = 14°
Therefore, the measure of each angle is 14°.
m∠1 = m∠3
(2x+26)° = (3x+32)°
Simplifying the equation:
2x + 26 = 3x + 32
Subtracting 2x from both sides:
26 = x + 32
Subtracting 32 from both sides:
-6 = x
Now that we know the value of x, we can substitute it back into either angle measure to find the actual measure of each angle, let's use m∠1:
m∠1 = (2x+26)°
m∠1 = (2(-6)+26)°
m∠1 = (-12+26)°
m∠1 = 14°
Therefore, the measure of each angle is 14°.