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

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Answer 1 · 2018-05-22T12:46:54

A=73
B=17

If angles are complementary, then they are found adjacent to each other in a right angle.

![https://useruploads.socratic.org/HqA6lzi3Ste1L44SSGY0_complementary_angle.jpg)

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#

Answer 2 · 2018-05-22T13:08:19

#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^@#