Answer:
Thus: m=14°, n=28°
Explanation:
Angles in a Circle
Let's review some concepts about angles in a circle.
The central angle 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°