The angle at the center is 50^. The angle at the circumference subtended by the same arc is half the angle at the center.

Here are the values of the angles:

• a)

  Step 1: The angle at the center is $50^\circ$. The angle at the circumference subtended by the same arc is half the angle at the center.

  $$a = \frac{1}{2} \times 50^\circ$$ $$a = 25^\circ$$ $$\boxed{a = 25^\circ}$$

• b)

  Step 1: The angle at the center is $120^\circ$. The angle at the circumference subtended by the same arc is half the angle at the center.

  $$b = \frac{1}{2} \times 120^\circ$$ $$b = 60^\circ$$ $$\boxed{b = 60^\circ}$$

• c)

  Step 1: The angle at the center is $140^\circ$. The angle at the circumference subtended by the same arc is half the angle at the center.

  $$c = \frac{1}{2} \times 140^\circ$$ $$c = 70^\circ$$ $$\boxed{c = 70^\circ}$$

• d)

  Step 1: The angle at the center is $180^\circ$ (a straight line). The angle at the circumference subtended by the same arc is half the angle at the center.

  $$d = \frac{1}{2} \times 180^\circ$$ $$d = 90^\circ$$ $$\boxed{d = 90^\circ}$$

• e)

  Step 1: The angle at the circumference is $30^\circ$. The angle at the center subtended by the same arc is twice the angle at the circumference.

  $$e = 2 \times 30^\circ$$ $$e = 60^\circ$$ $$\boxed{e = 60^\circ}$$

• f)

  Step 1: The angle at the circumference is $35^\circ$. The angle at the center subtended by the same arc is twice the angle at the circumference.

  $$f = 2 \times 35^\circ$$ $$f = 70^\circ$$ $$\boxed{f = 70^\circ}$$

• g)

  Step 1: Angles in the same segment are equal. Angle $g$ is subtended by the same arc as the $35^\circ$ angle at the circumference.

  $$g = 35^\circ$$ $$\boxed{g = 35^\circ}$$

• h)

  Step 1: The angle at the circumference is $25^\circ$. The angle at the center subtended by the same arc is twice the angle at the circumference.

  $$h = 2 \times 25^\circ$$ $$h = 50^\circ$$ $$\boxed{h = 50^\circ}$$

• i)

  Step 1: Angles in the same segment are equal. Angle $i$ is subtended by the same arc as the $25^\circ$ angle at the circumference.

  $$i = 25^\circ$$ $$\boxed{i = 25^\circ}$$

• j)

  Step 1: The angle at the circumference is $26^\circ$. The angle at the center subtended by the same arc is twice the angle at the circumference.

  $$j = 2 \times 26^\circ$$ $$j = 52^\circ$$ $$\boxed{j = 52^\circ}$$

• k)

  Step 1: Angles in the same segment are equal. Angle $k$ is subtended by the same arc as the $26^\circ$ angle at the circumference.

  $$k = 26^\circ$$ $$\boxed{k = 26^\circ}$$

• l)

  Step 1: The angle at the center is $140^\circ$. The angle at the circumference subtended by the same arc is half the angle at the center.

  $$l = \frac{1}{2} \times 140^\circ$$ $$l = 70^\circ$$ $$\boxed{l = 70^\circ}$$

• m)

  Step 1: The angle at the center is $140^\circ$. The angle at the circumference subtended by the same arc is half the angle at the center.

  $$m = \frac{1}{2} \times 140^\circ$$ $$m = 70^\circ$$ $$\boxed{m = 70^\circ}$$

• n)

  Step 1: Angles in the same segment are equal. Angle $n$ is subtended by the same arc as angles $l$ and $m$.

  $$n = 70^\circ$$ $$\boxed{n = 70^\circ}$$

• p)

  Step 1: The angle at the center is $130^\circ$. The angle at the circumference subtended by the same arc is half the angle at the center.

  $$p = \frac{1}{2} \times 130^\circ$$ $$p = 65^\circ$$ $$\boxed{p = 65^\circ}$$

• q)

  Step 1: Angles in the same segment are equal. Angle $q$ is subtended by the same arc as angle $p$.

  $$q = 65^\circ$$ $$\boxed{q = 65^\circ}$$

• r)

  Step 1: Angles in the same segment are equal. Angle $r$ is subtended by the same arc as angle $p$.

  $$r = 65^\circ$$ $$\boxed{r = 65^\circ}$$

• s)

  Step 1: The angle at the center is $100^\circ$. The angle at the circumference subtended by the same arc is half the angle at the center.

  $$s = \frac{1}{2} \times 100^\circ$$ $$s = 50^\circ$$ $$\boxed{s = 50^\circ}$$

• t)

  Step 1: The angle at the center is $100^\circ$. The angle at the circumference subtended by the same arc is half the angle at the center.

  $$t = \frac{1}{2} \times 100^\circ$$ $$t = 50^\circ$$ $$\boxed{t = 50^\circ}$$

• u)

  Step 1: Angles in the same segment are equal. Angle $u$ is subtended by the same arc as angles $s$ and $t$.

  $$u = 50^\circ$$ $$\boxed{u = 50^\circ}$$

• v)

  Step 1: The angle at the center is $160^\circ$. The angle at the circumference subtended by the same arc is half the angle at the center.

  $$v = \frac{1}{2} \times 160^\circ$$ $$v = 80^\circ$$ $$\boxed{v = 80^\circ}$$

• w)

  Step 1: The angle at the circumference is $40^\circ$. The angle at the center subtended by the same arc is twice the angle at the circumference.

  $$w = 2 \times 40^\circ$$ $$w = 80^\circ$$ $$\boxed{w = 80^\circ}$$

• x)

  Step 1: The angle at the center is $140^\circ$. The angle at the circumference subtended by the same arc is half the angle at the center.

  $$x = \frac{1}{2} \times 140^\circ$$ $$x = 70^\circ$$ $$\boxed{x = 70^\circ}$$

• y)

  Step 1: The angle at the center is $140^\circ$. The angle at the circumference subtended by the same arc is half the angle at the center.

  $$y = \frac{1}{2} \times 140^\circ$$ $$y = 70^\circ$$ $$\boxed{y = 70^\circ}$$

• z)

  Step 1: The angle at the center is $80^\circ$. The angle at the circumference subtended by the same arc is half the angle at the center.

  $$z = \frac{1}{2} \times 80^\circ$$ $$$$