If angle A and B are complementary and #A=5x+8# and #B=x+4#, what are the measurements of each angle?

Question

Theodore Abad · Accepted Answer

undefined If angles A and B are complementary, their measures sum up to 90 degrees. Given that A = 5x + 8 and B = x + 4:

$$ A + B = 5x + 8 + x + 4 = 90 $$

$$ 6x + 12 = 90 $$

$$ 6x = 90 - 12 $$

$$ 6x = 78 $$

$$ x = \frac{78}{6} $$

$$ x = 13 $$

Therefore, the measure of angle A:
$$ A = 5x + 8 = 5(13) + 8 = 65 + 8 = 73 $$

And the measure of angle B:
$$ B = x + 4 = 13 + 4 = 17 $$

Wyatt Anderson · Answer

A=73
B=17

If angles are complementary, then they are found adjacent to each other in a right angle. ![https://tutor.hix.ai) From above, you can see that A+B=90 So I can add my two angles together and have it equal to 90 #(5x+8)+(x+4)=90# #5x+8+x+4=90# #6x+12=90# #6x=90-12# #6x=78# #x=13# So #A=5x+8=5(13)+8=65+8=73# and #B=x+4=13+4=17# Just to make sure you are correct, add your A and B together and they should equal to 90 ie #A+B=73+17=90#

Aurora Ayala · Answer

#color(purple)(hat A = 73^@, color(brown)(hat B = 17^@# If two angles are to be complementary, thier sum equals #90^@# #hat A + hat B = 90^@# #hat A = 5x + 8, hat B = x + 4# #:. 5x + 8 + x + 4 = 90^@# #6x = 90 - 12 = 78# #x = 13# #color(purple)(hat A = 5x + 8 = 73^@# #color(brown)(hat B = x + 4 = 13 + 4 = 17^@#