Circles: Special Angles and Arcs in Circles

Think & Click: Angles Made by Chords, Secants and Tangents

Now, you try. Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

Find the value of x.

Circle with intersecting chords

3 x minus 5 equals one-half the quantity 142 plus 28; = 3 x minus 5 equals one-half of 170; 3 x minus 5 equals 85; 3 x equals 90; x equals 30

Find the measure of arc LT.

Circle with chords LU and TM that intersect at point C
Circle with intersecting chords

the measure of angle MCU equals one-half the quantity the measure of arc LT plus the measure of arc MU; 101 equals one-half the quantity the measure of arc LT plus 152; multiply both sides by 2; 202 equals the measure of arc LT plus 152; 50 degrees equals the measure of arc LT

Find the value of y.

Circle with secants intersecting outside the circle; intercepted arcs measure 105 degrees and 25 degrees; angle of intersection is 5y minus 10 degrees
Circle with secants that intersect outside the circle

5 y minus 10 equals one-half the quantity 105 minus 25; 5 y minus 10 equals one-half of 80; 5 y minus 10 equals 40; 5 y equals 50; y equals 10

Find the measure of angle J.

Circle with points H, K and F on the circle; tangent line JH and JK
Circle with two tangent lines

the measure of arc HK equals 360 minus the measure of arc HFK; the measure of arc HK equals 360 minus 225 equals 135 degrees; the measure of angle K equals one-half the quantity the measure of arc HFK minus the measure of arc HK; the measure of angle K equals one-half the quantity 225 minus 135; the measure of angle K equals one-half of 90; the measure of angle K equals 45 degrees

Find the value of a.

Circle with secants intersecting outside the circle; intercepted arcs measure 2a plus 39 degrees and 25 degrees; angle of intersection is 43 degrees
Circle with secants that intersect outside the circle

43 equals one-half the quantity 2 x plus 39 minus 25; 43 equals one-half the quantity 2a plus 14; 43 equals a plus 7; 36 equals

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