For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?(1 point) °
Since vertical angles are pairs of angles that share the same vertex and are formed by intersecting lines, they have equal measure.
So, we have the equation (2x+26)° = (3x+32)°.
We can solve for x by subtracting 2x from both sides of the equation:
26° = (3x+32)° - (2x+26)°
26° = x + 6°
Subtracting 6° from both sides:
20° = x
Now we can substitute x back into either angle measure equation to find the measure of the angles.
For m∠1:
m∠1 = (2x+26)°
m∠1 = (2*20+26)°
m∠1 = 40° + 26°
m∠1 = 66°
For m∠3:
m∠3 = (3x+32)°
m∠3 = (3*20+32)°
m∠3 = 60° + 32°
m∠3 = 92°
Therefore, the measure of angle 1 is 66° and the measure of angle 3 is 92°.