Free Printable WorksheetMathGeometryMath CurriculumG-C.A.3

GEO.118 Inscribed angles and intercepted arcs Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.118 Inscribed angles and intercepted arcs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.118 Inscribed angles and intercepted arcs - Primary standard selected for prompt fields in this prompt cell: CCSS G-C.A.3. Skill statement in this prompt cell: Select the correct inscribed-angle relationship and determine an unknown angle or arc measure. Associated standards listed with this skill in the curriculum source: CCSS G-C.A.3; FL MA.912.GR.5.3, 6.3; MA G-C.A.3; NY GEO G.G-C.A.3. 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.118 Inscribed angles and intercepted arcs skill assessments:

Problem 1Difficulty: Mastery
Points A, B, C, D, and E lie on a circle in that order. Arc AB = 36 degrees, arc BC = 64 degrees, arc CD = 82 degrees, arc DE = 48 degrees, and arc EA = 4x + 14 degrees. If angle ACE intercepts arc AE and measures 65 degrees, what is x?
A20
B24
C29
D32
Solution & Explanation:Angle ACE intercepts arc AE, so arc AE is 2 x 65 = 130 degrees. Solve 4x + 14 = 130, giving 4x = 116 and x = 29.
Problem 2Difficulty: Mastery
In a cyclic quadrilateral, m angle A : m angle C = 5 : 4. What is the measure of arc BCD intercepted by angle A?
A100 degrees
B180 degrees
C200 degrees
D225 degrees
Solution & Explanation:Opposite angles A and C are supplementary, so the 5:4 ratio represents 180 degrees total. One part is 20 degrees, so angle A = 5 x 20 = 100 degrees. The intercepted arc BCD is 2 x 100 = 200 degrees.
Problem 3Difficulty: Mastery
Angles TUV and TWV intercept the same arc TV. If m angle TUV = 7x - 4 degrees and m angle TWV = 4x + 20 degrees, what is m arc TV?
A52 degrees
B80 degrees
C104 degrees
D156 degrees
Solution & Explanation:Set the equal inscribed angles equal: 7x - 4 = 4x + 20, so x = 8. Each angle measures 7(8) - 4 = 52 degrees, so arc TV measures 2 x 52 = 104 degrees.

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Frequently Asked Questions

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QIs this GEO.118 Inscribed angles and intercepted arcs worksheet free for teachers and homeschoolers?

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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.A.3 (Primary standard selected for prompt fields in this prompt cell: CCSS G-C.A.3. Skill statement in this prompt cell: Select the correct inscribed-angle relationship and determine an unknown angle or arc measure. Associated standards listed with this skill in the curriculum source: CCSS G-C.A.3; FL MA.912.GR.5.3, 6.3; MA G-C.A.3; NY GEO G.G-C.A.3. Use this prompt-provided wording as the supporting standard description for this workflow.).

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