Q5. - Geometry

Question

Complete.

$\mathbf{m}\angle \mathbf{1}\mathbf{+}\mathbf{m}\angle \mathbf{2}\mathbf{=}\mathbf{m}\angle \underset{¯}{\mathbf{?}}$

Step-by-Step Solution

Answer

The complete statement is: $m\angle 1+m\angle 2\mathbf{=}m\angle \underset{¯}{\mathbf{JOT}}$.

Step 1. Write the Angle Addition Postulate.

The Angle Addition Postulate states that: 

If a point $B$ lies in the interior of $\angle \mathrm{AOC}$ then $\mathrm{m}\angle \mathrm{AOB}+\mathrm{m}\angle \mathrm{BOC}=\mathrm{m}\angle \mathrm{AOC}$.

Step 2. Observe the diagram.

The given diagram is:

From the given diagram, it can be noticed that:

$\begin{array}{l}m\angle JOK=m\angle 1\\ m\angle KOT=m\angle 2\end{array}$

Step 3. Write the equation expressing the relation between angles JOK, KOT, and JOT by using the Segment Addition Postulate.

From the given diagram it can be noticed that:

The point is lying in the interior of the angle $JOT$.

Therefore, by using the angle addition postulate:

$m\angle JOK+m\angle KOT=m\angle JOT$

Step 4. Substitute the values of angles JOK, KOT, and JOT in the above equation.

$\begin{array}{c}m\angle JOK+m\angle KOT=m\angle JOT\\ m\angle 1+m\angle 2=m\angle JOT\end{array}$

Step 5. Complete the given statement.

Therefore, the complete statement is $m\angle 1+m\angle 2=m\angle JOT$.