Sum and Difference of Angles: Angle bisector

$∢\text{ABD}=15$

BD bisects the angle.

Calculate the size of $∢\text{ABC}$.

$$

30

$∢DBC=90°$

BE cross $∢\text{DBA}$

Find the value $\alpha$

45

BO bisects $∢ABD$.

$∢\text{ABD}=85$

Calculate the size of

$\sphericalangle ABO\text{.}$

42.5

$∢\text{ABD}=90$

CB bisects $\sphericalangle\text{ABD}$.

$\sphericalangle\text{CBD}=\alpha$

Calculate the size of $∢ABC$.

45

BE bisects $∢\text{FBD}$.

$∢\text{FBE}=25$

Calculate the size of $∢\text{EBD}$.

25

$∢\text{AFB}=60$

$∢\text{AFE}=120$

$∢EFD=80$

FC bisects $∢DFB$.

Calculate the size of angle $∢\text{DFC}$

50

BD bisects $∢\text{ABC}$.

$∢EBC=\alpha$

$∢DBE=30$

Calculate the size of $∢\text{ABD}$.

$\alpha+30$

BD bisects $∢\text{ABC}$.

BE bisects$∢\text{ABD}$.

$∢\text{ABC}=50$

Calculate the size of $∢\text{ABE}$.

12.5

OC bisects $∢\text{DOB}$.

$∢KOD=2\alpha$

$∢DOC=\alpha$

$∢KOB=68$

Calculate the size of angle $∢\text{DOC}$ ($a$).

17