Question 126
Let $\Varangle A O B$ and $\Varangle B O C$ be adjacent supplementary angles such that the ratio of their measures is $\frac{1}{4}$. Let $[O D$ be the ray opposite to the bisector of the angle $\Varangle B O C$. Inside the angle $\Varangle C O D$ consider points $M$ and $N$ such that $m(\Varangle C O N)=m(\Varangle D O M)=2 \cdot m(\Varangle M O N)\gt 45^\circ$.
a) Find the measure of the angle $\Varangle C O D$.
b) Prove that the points $B, O, M$ are collinear.
a) Find the measure of the angle $\Varangle C O D$.
b) Prove that the points $B, O, M$ are collinear.