We are given a circle with center $O$. The measure of the central angle $\angle MON$ is $67^\circ$. We need to find the measure of the major arc $MDN$.

1. Problem Description

We are given a circle with center $O$. The measure of the central angle $\angle MON$ is $67^\circ$. We need to find the measure of the major arc $MDN$.

2. Solution Steps

The measure of the central angle is equal to the measure of the intercepted arc.

Therefore, the measure of minor arc $MN$ is $67^\circ$.

The entire circle has a measure of $360^\circ$.

The major arc $MDN$ is the rest of the circle besides the minor arc $MN$.

Therefore, the measure of major arc $MDN$ is the difference between the measure of the whole circle and the measure of the minor arc $MN$.

$m\widehat{MDN} = 360^\circ - m\widehat{MN}$

$m\widehat{MDN} = 360^\circ - 67^\circ$

$m\widehat{MDN} = 293^\circ$

3. Final Answer

The measure of arc $MDN$ is $293^\circ$.