What is the measure of two complementary angles if the measure of the larger angles is 12 more than twice the measure at the smaller angle?

Question

What is the measure of two complementary angles if the measure  of the larger angles is 12 more than twice the measure at the smaller angle?

Maverick Smith · Accepted Answer

The smaller angle is #26^@#
The larger angle is #64^@# Let #x# equal the number of degrees in the smaller angle. Smaller angle. . . . . . . . . . #x# #larr# smaller angle Twice that measure . . . #2x# 12 more than that . . . . . #2x + 12# #larr# larger angle Together, these two angles add up to #90^@# [small angle] plus [large angle ] #= 90# #[ . . . ( x ) . . .] . + . [ .(2x + 12) ] = 90# #(x) + (2x + 12) = 90# Solve for #x#, already defined as "the number of degrees in the smaller angle." 1) Combine like terms #3x + 12 = 90# 2) Subtract 12 from both sides to isolate the #3x# term #3x = 78# 3) Divide both sides by #3# to isolate #x#, already defined as "the number of degrees in the smaller angle" #x = 26# #larr# the number of degrees in the smaller angle Answer: The smaller angle is #26^@# So the larger angle must be #64^@# Check #26# plus #12# more than (#2# times #26#) should equal #90# #26 + 2(26) + 12# should equal #90# #26 + 52 + 12# should equal #90# #26 + 64# should equal #90# #90# does #= 90# Check!

Sadie Adams · Answer

undefined Let $ x $ represent the measure of the smaller angle. Then the measure of the larger angle is $ 2x + 12 $. Since the angles are complementary, their measures add up to $ 90^\circ $. So, we have the equation $ x + (2x + 12) = 90 $. Solving for $ x $, we find $ x = 26 $. Therefore, the measure of the smaller angle is $ 26^\circ $, and the measure of the larger angle is $ 2(26) + 12 = 64^\circ $.