# The chords KM and TP of the circle intersect at point A. Calculate the degree measure of the obtuse angle

The chords KM and TP of the circle intersect at point A. Calculate the degree measure of the obtuse angle formed by these chords, if K, M, T, P divide the circle into arcs, the degree mkry of which are proportional to the numbers 2,3,6,9

The full circle is 360 degrees.

Let the degree measure of the arc KT = 2 * X0, then, by condition, the arc TM = 3 * X0, MP = 6 * X0, KP = 9 * X0.

Then: 2 * X + 3 * X + 6 * X + 9 * X = 360.

20 * X = 360.

X = 360/20 = 180.

Then the degree measures of the arcs will be equal:

CT = 2 * 18 = 36.

TM = 3 * 18 = 54.

MP = 6 * 18 = 108.

KP = 9 * 18 = 162.

The value of the angle formed by the intersection of two arcs is equal to the half-sum of the degree measures of the opposite arcs.

Angle KAP = TAM = (KP + TM) / 2 = (162 + 54) / 2 = 108.

Answer: The obtuse angle between the chords is 108. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.