# #m/_A# and #m/_B# are complementary. #m/_A =3x -2# and #m/_B=x+4#. What is the value of each angle?

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To find the value of each angle, we need to solve for (x). Since angles (A) and (B) are complementary, their measures add up to (90^\circ).

Given that (m\angle A = 3x - 2) and (m\angle B = x + 4), we can set up the equation:

[ (3x - 2) + (x + 4) = 90 ]

Now, solve for (x):

[ 3x - 2 + x + 4 = 90 ] [ 4x + 2 = 90 ] [ 4x = 88 ] [ x = 22 ]

Now that we have found (x = 22), we can substitute it back into the expressions for the measures of angles (A) and (B) to find their values:

[ m\angle A = 3(22) - 2 = 66 - 2 = 64^\circ ] [ m\angle B = 22 + 4 = 26^\circ ]

Therefore, the measure of angle (A) is (64^\circ) and the measure of angle (B) is (26^\circ).

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