Question 157
Consider the adjacent angles $\angle A O B$ and $\angle B O C$ such that their bisectors $[OM$ and $[ON$ form an angle of $75^{\circ}$.
a) Determine $m(\angle A O B)$ and $m(\angle B O C)$, given that $3 \cdot m(\angle A O B)=2 \cdot m(\angle B O C)$.
b) Suppose the ray $[OT$ forms a right angle with the ray $[OM$, such that the points $M$ and $T$ lie on the same side as the point $B$ with respect to the line $OA$. Compute: $m(\angle T O N)$, $m(\angle B O N)$, $m(\angle B O T)$ and $m(\angle C O T)$.
a) Determine $m(\angle A O B)$ and $m(\angle B O C)$, given that $3 \cdot m(\angle A O B)=2 \cdot m(\angle B O C)$.
b) Suppose the ray $[OT$ forms a right angle with the ray $[OM$, such that the points $M$ and $T$ lie on the same side as the point $B$ with respect to the line $OA$. Compute: $m(\angle T O N)$, $m(\angle B O N)$, $m(\angle B O T)$ and $m(\angle C O T)$.