Free Printable WorksheetMathGeometryMath CurriculumG-C.B.5

GEO.121 Angles formed by chords, secants, and tangents Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.121 Angles formed by chords, secants, and tangents. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.121 Angles formed by chords, secants, and tangents - Primary standard selected for prompt fields in this prompt cell: CCSS G-C.B.5. Skill statement in this prompt cell: Select the correct arc-based formula and determine the measure of an angle formed by chords, secants, or tangents. Associated standards listed with this skill in the curriculum source: CCSS G-C.B.5; FL MA.912.GR.6.4; MA G-C.B.5; NY GEO G.G-C.B.5. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Geometry

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related GEO.121 Angles formed by chords, secants, and tangents skill assessments:

Problem 1Difficulty: Mastery

A review card lists formulas for circle angles. Which card is correct?

ATangent-chord: half the intercepted arc; inside chords: half the sum of the two intercepted arcs; exterior secants or tangent-secant: half the difference of intercepted arcs

BTangent-chord: half the difference of arcs; inside chords: half the intercepted arc; exterior secants: half the sum of arcs

CTangent-chord: full intercepted arc; inside chords: arc difference; exterior secants: arc sum

DTangent-chord: 180 degrees minus the arc; inside chords: half the major arc; exterior secants: half the minor arc

Solution & Explanation:The correct card matches the location of the vertex: tangent-chord on the circle uses half one intercepted arc, chords inside use half a sum, and exterior secants or tangent-secants use half a difference.

Problem 2Difficulty: Mastery

Which configuration gives the largest angle measure?

AA tangent-chord angle intercepts an arc of 132 degrees

BTwo chords intersect inside using arcs 70 degrees and 80 degrees

CTwo secants meet outside using arcs 218 degrees and 76 degrees

DTwo tangents meet outside with minor arc 96 degrees

Solution & Explanation:Compute each angle: tangent-chord 132/2 = 66; inside chords (70 + 80)/2 = 75; exterior secants (218 - 76)/2 = 71; two tangents 180 - 96 = 84. The largest is 84 degrees.

Problem 3Difficulty: Mastery

Two secants from an outside point intercept arcs with equal measures. Which statement correctly describes the exterior angle?

AThe exterior angle is 0 degrees by the formula, so a nondegenerate secant angle needs different intercepted arc measures.

BThe exterior angle is 90 degrees because equal arcs always form right angles.

CThe exterior angle equals one of the intercepted arcs.

DThe exterior angle equals the sum of the intercepted arcs.

Solution & Explanation:The exterior secant angle is half the difference of the arcs. If the arcs are equal, the difference is 0, so the formula gives 0 degrees.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Geometry Math students. It aligns with educational standard G-C.B.5 (Primary standard selected for prompt fields in this prompt cell: CCSS G-C.B.5. Skill statement in this prompt cell: Select the correct arc-based formula and determine the measure of an angle formed by chords, secants, or tangents. Associated standards listed with this skill in the curriculum source: CCSS G-C.B.5; FL MA.912.GR.6.4; MA G-C.B.5; NY GEO G.G-C.B.5. Use this prompt-provided wording as the supporting standard description for this workflow.).