91Ó°ÊÓ

Diameter figure is shown below.

$m∠A=35$

We use basic geometric and angle concept

In $\mathrm{Δ}AOB$.

$OA=OB                    ∴\left(\text{Radius}\right)$

If two sides are equal in triangle, then angle opposite to these sides are also equal.

$\begin{array}{l}m∠B=m∠A\\ m∠B=n\end{array}$

And

$\begin{array}{l}m∠B+m∠A+∠AOB=180\\ n+n+∠AOB=180\\ ∠AOB=180−2n\end{array}$

Since, AOC is a straight line therefore,

$\begin{array}{l}∠AOB+∠BOC=180\\ \left(180−2n\right)+∠BOC=180\\ ∠BOC=2n\end{array}$

Measure of arc BC is the central angle.

$\begin{array}{l}m\stackrel{Áåœ}{BC}=m∠BOC\\ m\stackrel{Áåœ}{BC}=2n\end{array}$

Therefore, the answer is$\left(180-2n\right),2n\text{and}2n$.

$m\stackrel{Áåœ}{BC}=6k$

We use basic geometric and angle concept

Measure of arc BC is the central angle.

$\begin{array}{l}m\stackrel{Áåœ}{BC}=m∠BOC\\ m∠BOC=6k\end{array}$

Since, AOC is a straight line therefore,

$\begin{array}{l}∠AOB+∠BOC=180\\ ∠AOB+6k=180\\ ∠AOB=180−6k\end{array}$

In$\mathrm{Δ}AOB$.

$OA=OB\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}∴\left(\text{Radius}\right)$

If two sides are equal in triangle, then angle opposite to these sides are also equal.

$m∠B=m∠A$

And

$\begin{array}{l}m∠B+m∠A+∠AOB=180\\ m∠A+m∠A+\left(180−6k\right)=180\\ 2∠A=6k\\ ∠A=3k\end{array}$

Therefore, the answer is $3k$.