Grade 10 · Math · Geometry

10th grade Angles formed by chords, secants and tangents worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Angles formed by chords, secants and tangents

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

Kira cuts two straight lines across a round pizza. Chords CF and DG cross at H, inside circle O. What is ∠CHD, in degrees?
Luz draws two crossing chords on a clock face. Chords CF and DG cross at H, inside circle O. What is ∠CHD, in degrees?
Milo pipes two crossing lines of icing on a cookie. Chords CF and DG cross at H, inside circle O. What is ∠CHD, in degrees?
Noah sews two crossing stripes on a round rug. Chords CF and DG cross at H, inside circle O. What is ∠CHD, in degrees?
Pia rolls a play ball on a straight floor, touching at C. Chord CD meets the tangent at C, and arc CD inside the angle is 110°. What is that angle, in degrees?
Ren draws a bike wheel touching the road at C. Chord CD meets the tangent at C, and arc CD inside the angle is 76°. What is that angle, in degrees?
Tala lays a ruler touching a drum at C. Chord CD meets the tangent at C, and arc CD inside the angle is 152°. What is that angle, in degrees?
Zee rests a stick against a round plate at C. Chord CD meets the tangent at C, and arc CD inside the angle is 98°. What is that angle, in degrees?
Bo draws two lines from Q through a clock face. Secants QCD and QGF meet at Q, outside circle O. What is ∠Q, in degrees?
Esme cuts two straight lines from Q through a round pizza. Secants QCD and QGF meet at Q, outside circle O. What is ∠Q, in degrees?

Angles formed by chords, secants and tangents. Every version has 10 questions, and the answer key prints on the second page.

I can find the angle where two chords cross: half the sum of the arcs.
I can find the angle made outside the circle: half the difference of the arcs.
I can find an angle made by a tangent and a chord, and work back to a missing arc.

Standard: G-C.A.2

secant: A line that cuts through the circle at two points.

tangent-chord angle: The angle between a tangent and a chord at the point of tangency.

vertical angles: The two opposite angles where two lines cross; they are equal.

far arc / near arc: From an outside point, the arc farther away / nearer.

half the sum / half the difference: (arc + arc) ÷ 2 inside; (far − near) ÷ 2 outside.

Your child used the outside-angle rule (half the difference) for chords that cross inside the circle.

Your child found the right arcs but did not take half.

Your child made the angle between a tangent and a chord equal to its arc.

Ask: where do the two lines meet, inside or outside the circle?

Ask: is an angle made by two lines bigger or smaller than the arcs it catches?

Ask: where is the corner of this angle, at the center or on the circle?

What is the most common mistake with angles formed by chords, secants and tangents?

Your child used the outside-angle rule (half the difference) for chords that cross inside the circle.

How can I help my child with angles formed by chords, secants and tangents?

Ask: where do the two lines meet, inside or outside the circle?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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