Answer:
<em>Thus: m=14°, n=28°</em>
Step-by-step explanation:
<u>Angles in a Circle</u>
Let's review some concepts about angles in a circle.
The <em>central angle </em>is formed between two radii and its vertex lie at the center of the circle.
The inscribed angle is formed between two chords whose vertex lies on the circumference of a circle.
The measure of a central angle x formed by the same lines that define an inscribed angle y is:
x = 2y
Following the definitions and relations above, we find that:
- The measure of the central angle 98° is double the inscribed angle 35°+m
- The measure of the central angle n is double the inscribed angle m
The first statement leads to:
98 = 2 (35+m)
Dividing by 2:
49 = 35 + m
m = 49 - 35 = 14
m = 14°
The second statement leads to:
n = 2m = 28°
Thus: m=14°, n=28°
