Grade 10 · Geometry & measurement

Circle theorems practice

Circle theorems is a grade 10 math skill aligned to Common Core standard HSG.C.A.2: identify and describe relationships among inscribed angles, radii, and chords. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 15 circle theorems problems our math games drill.

CCSS HSG.C.A.215 questions in the bank

Sample questions

Try 8 for free

Question 1easy

A central angle measures $75°$ . What is the measure of its intercepted arc?

A central angle equals its intercepted arc, so the arc is $75°$ .

Question 2easy

An inscribed angle intercepts an arc of $140°$ . What is the inscribed angle?

Inscribed angle $= \dfrac{140}{2} = 70°$ .

Question 3easy

An inscribed angle is $35°$ . What is the measure of its intercepted arc?

The intercepted arc is twice the inscribed angle: $2 \times 35 = 70°$ .

Question 4easy

An inscribed angle intercepts an arc of $50°$ . What is the inscribed angle?

Inscribed angle $= \dfrac{50}{2} = 25°$ .

Question 5easy

An inscribed angle intercepts an arc of $100°$ . What is the inscribed angle?

An inscribed angle is half its intercepted arc: $\dfrac{100}{2} = 50°$ .

Question 6easy

An inscribed angle intercepts an arc of $60°$ . What is the inscribed angle?

An inscribed angle is half its intercepted arc: $\dfrac{60}{2} = 30°$ .

Question 7easy

An inscribed angle intercepts an arc of $120°$ . What is the inscribed angle?

An inscribed angle is half its intercepted arc: $\dfrac{120}{2} = 60°$ .

Question 8easy

An inscribed angle is $45°$ . What is the measure of its intercepted arc?

The intercepted arc is twice the inscribed angle: $2 \times 45 = 90°$ .

Tests that cover circle theorems:

SAT ACT ACT Aspire LEAP 2025 MCAP

More Grade 10 skills:

Circle equation translations Equation of a circle Advanced area formulas Midpoint formula Normal distribution basics Unit circle trig values (SAT)Perimeter and arc length Similar right triangle trigonometry All Grade 10 practice →

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