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Given: ∠AOC and ∠BOC are complementary.
m∠AOC=m∠BOC+30°
Find: m∠AOC and m∠BOC


Statement Reason
1. m∠AOC+m∠______ = ______ 1. _____________
2. m∠______ + ______ +m∠BOC=90°
2. Substitution
3. m∠BOC = _________ 3. Algebra
4. m∠AOC = _________ 4. Algebra

Respuesta :

MrRoyal

Answer:

[tex]AOC = 60[/tex]

[tex]BOC = 30[/tex]

Explanation:

Given

Complementary Angles: AOC & BOC

[tex]AOC = BOC + 30[/tex]

Required

Determine AOC and BOC

[tex]AOC + BOC = 90[/tex] ---- Complementary Angles

Substitute BOC + 30 for AOC

[tex]BOC + 30 + BOC = 90[/tex]

Collect Like Terms

[tex]BOC + BOC = 90 - 30[/tex]

[tex]2BOC = 60[/tex]

Divide through by 2

[tex]BOC = 30[/tex]

Recall that [tex]AOC = BOC + 30[/tex]

[tex]AOC = 30 + 30[/tex]

[tex]AOC = 60[/tex]

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