Q33 - Geometry

Question

Given the diagram, state whether you can reach the conclusion shown.

$m\angle AOF\simeq 130$

Step-by-Step Solution

Answer

We can conclude that $\mathit{m}\mathbf{\angle }\mathit{A}\mathit{O}\mathit{F}\mathbf{\simeq }\mathbf{130}$

Step 1. Observe the given diagram.

Step 2. Highlight the ∠AOF in the given diagram.

Step 3. Explain whether you can reach the given conclusion.

As $\angle AOC\cong \angle BOC$ implies that $m\angle AOC=\angle BOC=90°$ and it is given in the figure that $m\angle BOF=50°$

$\angle AOB$ is a straight angle, that is,  and it can be written as 

$\begin{array}{l}m\angle AOB=m\angle AOC+m\angle BOC\\ =m\angle AOC+m\angle COF+m\angle BOF\end{array}$

Then,

$\begin{array}{l} 180=90+m\angle COF+50\\ m\angle COF=180-90-50\\ =40°\end{array}$

$\angle AOF$ can be written as 

$\begin{array}{l}m\angle AOF=m\angle AOC+m\angle COF\\ =90+40\\ =130°\end{array}$

Therefore we can conclude that, $m\angle AOF\simeq 130$.