For two vertical angles with measures m∠1 = (4x + 26) ° and m∠3 = (3x + 32) ° , what is the measure of each angle?(1 point) Responses 6° 6degree 24° 24degree 50° 50degree 64°
The measure of each angle is 64°.
are you sure
I apologize for the confusion. Since the two angles are vertical angles, they are congruent. So, we can set up an equation and solve for x.
m∠1 = m∠3
4x + 26 = 3x + 32
Subtract 3x from both sides:
4x - 3x + 26 = 3x - 3x + 32
x + 26 = 32
Subtract 26 from both sides:
x + 26 - 26 = 32 - 26
x = 6
Now we can substitute the value of x back into the expressions for the angles:
m∠1 = 4x + 26 = 4(6) + 26 = 24 + 26 = 50°
m∠3 = 3x + 32 = 3(6) + 32 = 18 + 32 = 50°
So, the measure of each angle is 50°.
are you sure
I apologize for the incorrect response earlier. Let's solve the problem again:
Since the two angles are vertical angles, they are congruent. So, we can set up an equation and solve for x.
m∠1 = m∠3
4x + 26 = 3x + 32
Subtract 3x from both sides:
4x - 3x + 26 = 3x - 3x + 32
x + 26 = 32
Subtract 26 from both sides:
x + 26 - 26 = 32 - 26
x = 6
Now we can substitute the value of x back into the expressions for the angles:
m∠1 = 4x + 26 = 4(6) + 26 = 24 + 26 = 50°
m∠3 = 3x + 32 = 3(6) + 32 = 18 + 32 = 50°
So, the measure of each angle is 50°.