If arc KJ = 13x-10 and arc JI = 7x-10, then find the m∠KIJ
.120 degrees
120 degrees
60 degrees
60 degrees
80 degrees
80 degrees
10 degrees
The sum of the measures of two arcs of a circle that intersect at a common endpoint is equal to the measure of the angle formed by the two arcs at that common endpoint.
Given that arc KJ = 13x - 10 and arc JI = 7x - 10, we can set up the equation:
13x - 10 + 7x - 10 = m angle KIJ
Combining like terms, we get:
20x - 20 = m angle KIJ
Since the sum of the angles in a triangle is 180 degrees, we know that:
m angle KIJ = 180 - 13 - 20
m angle KIJ = 180 - 120
m angle KIJ = 60 degrees
Therefore, the measure of angle KIJ is 60 degrees.