Vertical angles are opposite angles formed by two intersecting lines. They have equal measures.
Therefore, we can set the measures of the two vertical angles equal to each other:
(2x + 26)° = (3x + 32)°
Now, we can solve for x:
2x + 26 = 3x + 32
-2x - 2x = 32 - 26
-4x = 6
x = -6/4
x = -3/2
Now, we substitute this value of x back into either of the angle measures to find the measure of each angle.
Let's use the first angle measure:
m∠1 = (2x + 26)°
m∠1 = (2(-3/2) + 26)°
m∠1 = (-3 + 26)°
m∠1 = 23°
Therefore, the measure of each angle is 23°.
for two vertical angles with measures m∠1 = (2x + 26)° and m∠3 = (3x + 32)° , what is the measure of each angle?
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