An angle is 74 degrees more than its complement. Find both angles.

Complementary angles equal 90°

x= angle 1
x+74= angle 2

x + (x+74)= 90°
combine like terms
2x+74= 90
subtract 74 from both sides
2x=16
divide both sides by 2
x=8° angle 1

Substitute x=8 to find angle 2
=x+74
=8+74
=82° angle 2

Check:
angle 1 + angle 2= 90°
8° + 82°= 90°
90°=90°

Hope this helps! :)

Answer Link

shrutiagrawal1798 shrutiagrawal1798 · Answer 2 · 2021-11-11T13:53:59+01:00

The complementary angle defined as the angles which measures add up to [tex]90^{\circ}[/tex].

The angles are [tex]8^{\circ}[/tex] and [tex]82^{\circ}[/tex].

Given:

An angle is [tex]74^{\circ}[/tex] more than its complement.

Let angle 1 is [tex]x[/tex].

Angle 2 is [tex]x+74^{\circ}[/tex].

As per complementary angle definition,

[tex]\begin {aligned}\\x+x+74^{\circ}=90^{\circ}\\2x=90^{\circ}-74^{\circ}\\2x=16^{\circ}\\x=8^{\circ}\\\end[/tex]

Substitute [tex]x=8^{\circ}[/tex] to find angle 2.

[tex]8^{\circ}+74^{\circ}=82^{\circ}[/tex]

Thus, the angles are [tex]8^{\circ}[/tex] and [tex]82^{\circ}[/tex].

Learn more about Complementary here:

https://brainly.com/question/9243926