Question

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

Answer 1

$\begin{gathered} 1.\measuredangle AOC+\measuredangle BOC=90\text{ complementay angles} \\ 2.\measuredangle BOC+\measuredangle BOC+30=90\text{ substitution} \\ 3.\text{ }\measuredangle BOC=30 \\ 4.\measuredangle AOC=60 \end{gathered}$

Explanation

Two Angles are Complementary when they add up to 90 degrees

Step 1

Let

$\begin{gathered} \measuredangle AOC\text{ +}\measuredangle BOC\text{ are complementary, then} \\ \measuredangle AOC\text{ +}\measuredangle BOC=90 \\ \text{reason, the angles are complementary} \end{gathered}$

Step 2

2. and 3.

$\begin{gathered} \measuredangle AOC\text{ +}\measuredangle BOC=90\text{ equation (1)} \\ \text{also} \\ \measuredangle AOC=\measuredangle BOC+30\text{ equation (2)} \\ \text{replace equation }(2)\text{ in (1}= \\ \text{then} \\ \\ \measuredangle BOC+30+\measuredangle BOC=90 \\ 2\measuredangle BOC+30=90 \\ 2\measuredangle BOC=90-30 \\ 2\measuredangle BOC=60 \\ \measuredangle BOC=30 \\ \end{gathered}$

Step 3

4.

finally, replace the value of BOC to find angle AOC

$\begin{gathered} \measuredangle AOC=\measuredangle BOC+30\text{ equation (2)} \\ \measuredangle AOC=\measuredangle BOC+30\text{ } \\ \measuredangle AOC=30+30\text{ } \\ \measuredangle AOC=60 \\ \end{gathered}$

I hope this helps you