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Answer :
Final answer:
In the given figure, we have a circle with center O and three radii OC, OB, and OE dividing the circle into three sectors COB, BOE, and EOC. Tangents ACD, ABF, and DEF are drawn, intersecting the exterior at points A, D, and F. We are given that the exterior angle D measures 124 degrees and the exterior angle A measures 114 degrees.
Explanation:
In the given figure, we have a circle with center O and three radii OC, OB, and OE dividing the circle into three sectors COB, BOE, and EOC. Tangents ACD, ABF, and DEF are drawn, intersecting the exterior at points A, D, and F. We are given that the exterior angle D measures 124 degrees and the exterior angle A measures 114 degrees. We need to match the angles and arcs to their measures.
Let's denote the measures of angles COB, BOE, and EOC as x, y, and z, respectively, and the measures of the arcs CA, BA, and EA as m, n, and p, respectively.
Since the tangents intersect the exterior at the points A, D, and F, we have the following relationships between the angles and arcs:
x + m = 114
z + n = 124
x + y + z = 360 (the sum of the angles in a circle)
By solving this system of equations, we can find the values of x, y, and z, and match them with the corresponding measures of the arcs.
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Rewritten by : Jeany
