Question

BM 1: 2. Find the value of angles x and y in circle A.

.X=
150°
175°
y =
to

Answer 1

x=35 y=17.5

Explanation:

This problem wants you to find the angles of an inscribed and central angle.

Note: central angles are angles that have radii as there sides and the center (of the circle) as its center. Inscribed angles are angles that have chords as there sides and there vertex as a point on a circle.

I will by find the measure of the missing arc. To do this is simple, Just add 175+150 and subtract from 360,

175+150= 325

360-325=35

So, the missing arc length is 35. X is a central angle and central angles are equal to the arc length. This means that,

x=35

Lastly, we need to find y, an inscribed angle. Inscribed angles are half of the arc length. So, the measure of y is 17.5

y=17.5

Answer 2

x = 35

y = 17.5

Explanation:

By Central angle and its corresponding arc theorem:

x° = 360° - (175° + 150°)

x° = 360° - 325°

x° = 35°

x = 35

By inscribed angle theorem:

`y \degree = (1)/(2) x \\ \\ y\degree = (1)/(2) * 35 \degree \\ \\ y\degree = 17.5 \degree \\ \\ y \: = 17.5`