Vertical angles are always congruent, meaning they have the same measure. Therefore, we can set the two angle measures equal to each other and solve for x:
(2x + 26) = (3x + 32)
2x + 26 = 3x + 32
Subtract 2x from both sides:
26 = x + 32
Subtract 32 from both sides:
-6 = x
Now that we have found the value of x, we can substitute it back into either angle measure to find the measure of each angle:
m∠1 = 2(-6) + 26
m∠1 = -12 + 26
m∠1 = 14
Therefore, the measure of angle 1 is 14 degrees.
Now we can use the value of x to find the measure of angle 3:
m∠3 = 3(-6) + 32
m∠3 = -18 + 32
m∠3 = 14
Therefore, the measure of angle 3 is also 14 degrees.
For two vertical angles with measures m∠1=(2x+26) and m∠3=(3x+32), what is the measure of each angle?
1 answer
1 answer