Find x & Complementary Angles

[nycmath]

See attachment.

[Eigenvalue]

[tex]\angle[/tex]DAC and [tex]\angle[/tex]CAB are complementary
m[tex]\angle[/tex]DAC+m[tex]\angle[/tex]CAB=90°
m[tex]\angle[/tex]DAC=x°
m[tex]\angle[/tex]CAB=(x²)°

Substitute in the values for [tex]\angle[/tex]DAC and [tex]\angle[/tex]CAB
x°+(x²)°=90°
x+x²=90

Subtract 90 from both sides:
x²+x-90=0

Factor:
(x+10)(x-9)=0

x=9, as an angle measure cannot be negative
m[tex]\angle[/tex]DAC=9°
m[tex]\angle[/tex]CAB=81°

[nycmath]

[tex]\angle[/tex]DAC and [tex]\angle[/tex]CAB are complementary
m[tex]\angle[/tex]DAC+m[tex]\angle[/tex]CAB=90°
m[tex]\angle[/tex]DAC=x°
m[tex]\angle[/tex]CAB=(x²)°

Substitute in the values for [tex]\angle[/tex]DAC and [tex]\angle[/tex]CAB
x°+(x²)°=90°
x+x²=90

Subtract 90 from both sides:
x²+x-90=0

Factor:
(x+10)(x-9)=0

x=9, as an angle measure cannot be negative
m[tex]\angle[/tex]DAC=9°
m[tex]\angle[/tex]CAB=81°

Isn't geometry fun?