∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5, and m∠JKL = x − 1. Find the measure of each angle.

complimentary angles, when added, will equal 90 degrees
so < DFG and < JKL, when added = 90
x + 5 + x - 1 = 90
2x + 4 = 90
2x = 90 - 4
2x = 86
x = 86/2
x = 43

< DFG = x + 5......43 + 5 = 48 degrees <==
< JKL = x - 1........43 - 1 = 42 degrees <==

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lisboa lisboa · Answer 2 · 2021-10-01T14:10:59+02:00

∠DFG and ∠JKL are complementary angles

Measure of each angle

[tex]m<DFG=48\\m<JKL= 42[/tex]

Given :

∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5,

and m∠JKL = x − 1

When two angles are complementary then the sum of angles is 90 degrees

∠DFG and ∠JKL are complementary angles.

So, [tex]m<DFG+m<JKL =90[/tex]

Now replace the expressions and solve for x

[tex]x+5+x-1=90\\2x+4=90\\2x=90-4\\2x=86\\x=43[/tex]

Now replace x with 43 and find out each angle

[tex]m<DFG= x+5\\m<DFG= 43+5=48\\\\m<DFG=48\\m<JKL=x-1=43-1=42[/tex]

[tex]m<DFG=48\\m<JKL= 42[/tex]

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