Vertical angles are formed by two intersecting lines and are always congruent. Therefore, we can set up an equation and solve for x to find the value of each angle.
Since vertical angles are congruent, we have:
m<1 = m<3
(2x + 26) = (3x + 32)
Rearranging to isolate terms with x:
2x - 3x = 32 - 26
-x = 6
Dividing both sides by -1 to solve for x:
x = -6
Now we can substitute x back into either m<1 or m<3 to find the measure of each angle. Let's use m<1:
m<1 = 2x + 26 = 2(-6) + 26 = -12 + 26 = 14
Therefore, the measure of angle 1 (<1) is 14 degrees.
Since vertical angles are congruent, the measure of angle 3 (<3) is also 14 degrees.
For two verticle angles with measures m<1=(2x+26) and m<3=(3x+32) what is the measure of each angle?
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