For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?
Vertical angles are formed when two lines intersect. They are always congruent, which means they have the same measure.
In this case, we have two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)°.
Therefore, we can set up an equation: (2x+26)° = (3x+32)°.
Now, we can solve for x:
2x+26 = 3x+32
Subtract 2x from both sides:
26 = x+32
Subtract 32 from both sides:
-6 = x
Now, we can substitute this value of x back into either of the expressions for the angles to find their measures.
Let's substitute it into m∠1=(2x+26)°:
m∠1 = 2(-6)+26
= -12+26
= 14
Thus, the measure of angle 1 is 14°.
Since vertical angles are congruent, the measure of angle 3 will also be 14°.