For two vertical angles with measures m∠1 = (4x + 26)°
°
and m∠3 = (3x + 32)°
°
, what is the measure of each angle?
Vertical angles are two angles that share the same vertex and are opposite each other when two lines intersect.
Since ∠1 and ∠3 are vertical angles, they are congruent.
So, we can set up an equation to solve for x:
4x + 26 = 3x + 32
Simplifying the equation:
4x - 3x = 32 - 26
x = 6
Now, we can substitute the value of x back into the expressions for ∠1 and ∠3 to find their measures:
m∠1 = (4x + 26)° = (4(6) + 26)° = 24 + 26 = 50°
m∠3 = (3x + 32)° = (3(6) + 32)° = 18 + 32 = 50°
Therefore, the measure of each angle is 50°.