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. $$z = \frac{1}{2} \times 80^\circ$$ $$z = 4