Question

Two chords intersect within a circle to form an angle whose measure is 53 degrees. If the arcs are represented by 3x+3 and 10x-14, find the measure of the LARGER of these two arcs.

Answer 1

76degrees

Explanation:

Using the theorem which states that the vertex of the angle inside a circle is half the sum of the measured intercepted arcs. Hence;

Angle at the vertex = 53 degrees

Half the sum of intercepted arcs = 1/2(3x+3+10x-14)

Half the sum of intercepted arcs = 1/2(13x-11)

Equating to the vertex to find x

1/2(13x-11) = 53

13x - 11 = 2 * 53

13x - 11 = 106

13x = 106 + 11

13x = 117

x = 117/13

x = 9

For the arc 3x + 3

= 3(9) + 3

= 27 + 3

= 30degrees

For the arc 10x - 14

= 10(9) - 14

= 90 - 14

= 76degrees

Hence the measure of the larger of the two arcs is 76degrees