How do I solve these with steps

[misty cypress]

Please give me answers but walk me through on how to do them that way I learn faster ty for any help ☺️

[safe oracle]

How do I solve these with steps

[glass karma]

$\angle{A},\angle{B},\angle{C},\angle{D}$ are inscribed angles, meaning that their measures are equal to half the measures of their intercepted arcs.

For example,

$\newline\angle{A}=\frac{1}{2}\cdot\overset{\huge\frown}{BD}$

[ashen sun]

solarunes

[glossy cedar]

so basically, opposite angles in an inscribed quadrilateral of a circle are supplementary

so angle D is 115 degrees

Also, inscribed angle measures are half of their intercepted arc measures

so if arc BC is 65 degrees and arc CD is 149 degrees, we add them up

and get 214 degrees

half that, and we have 107 degrees for angle A

angle C is supplementary to A, so it is 73 degrees

For the second one, we know that if a radius is perpendicular to a chord, then it bisects the chord into congruent segments

so the right triangle has measures x, 10.9, and 12.6

we can use pythagorean theorem to find x

(12.6)^2-(10.9)^2=x^2, or 39.95

square root both sides, and you get x is about 6.3206012372241930573281107524048