Math by First Principles
Level 1 · Foundational ← Back to lesson

Inscribed Angles: Practice

12 multiple-choice questions, progressively harder.

Level 1 · Foundational 0 / 12 answered
Question 1 of 12
  1. 1

    Which description defines an inscribed angle?

  2. 2

    Points A,V,B,WA,V,B,W occur in that order around a circle. Which arc is intercepted by ∠AVB\angle AVB?

    A, V, B, W occur in order on the circle.A, V, B, W occur in order on the circle. Exact angle and arc measures come from the statement; the schematic preserves the stated incidence and point order.AVBWSchematic; use the stated givens.
  3. 3

    An inscribed angle intercepts an arc of 132∘132^\circ. What is its measure?

  4. 4

    An inscribed angle measures 41∘41^\circ. What is the measure of its intercepted arc?

  5. 5

    The major arc AXBAXB excluding VV measures 238∘238^\circ. Find m∠AVBm\angle AVB.

    V lies on the short arc AB, and X lies on the major arc AB.V lies on the short arc AB, and X lies on the major arc AB. Exact angle and arc measures come from the statement; the schematic preserves the stated incidence and point order.AVBXSchematic; use the stated givens.
  6. 6

    ABAB is a diameter, and CC is another point on the circle. Find m∠ACBm\angle ACB.

    AB is a diameter with center O, and C is another point on the circle.AB is a diameter with center O, and C is another point on the circle. Exact angle and arc measures come from the statement; the schematic preserves the stated incidence and point order.ABCOSchematic; use the stated givens.
  7. 7

    Distinct points A,B,CA,B,C lie on a circle. If m∠ABC=90∘m\angle ABC=90^\circ, which segment is a diameter?

  8. 8

    P,QP,Q lie on the same open arc between A,BA,B. If m∠APB=57∘m\angle APB=57^\circ, find m∠AQBm\angle AQB.

    P and Q lie on major arc AB; R lies on minor arc AB. The three vertices exclude different arcs.P and Q lie on major arc AB; R lies on minor arc AB. The three vertices exclude different arcs. Exact angle and arc measures come from the statement; the schematic preserves the stated incidence and point order.ABPQRSchematic; use the stated givens.
  9. 9

    P,RP,R lie on opposite open arcs between A,BA,B. If m∠APB=39∘m\angle APB=39^\circ, find m∠ARBm\angle ARB.

    P and Q lie on major arc AB; R lies on minor arc AB. The three vertices exclude different arcs.P and Q lie on major arc AB; R lies on minor arc AB. The three vertices exclude different arcs. Exact angle and arc measures come from the statement; the schematic preserves the stated incidence and point order.ABPQRSchematic; use the stated givens.
  10. 10

    Minor arc TATA measures 116∘116^\circ. Ray TRTR is tangent at TT on the same side of line OTOT as AA. Find m∠RTAm\angle RTA.

    TR and TS are opposite tangent rays at T. R and A lie on the same side of line OT.TR and TS are opposite tangent rays at T. R and A lie on the same side of line OT. Exact angle and arc measures come from the statement; the schematic preserves the stated incidence and point order.TAORSSchematic; use the stated givens.
  11. 11

    Major arc TBATBA measures 226∘226^\circ. Ray TSTS is tangent at TT on the opposite side of line OTOT from AA. Find m∠STAm\angle STA.

    B lies on major arc TA. TS is the tangent ray opposite A across line OT.B lies on major arc TA. TS is the tangent ray opposite A across line OT. The schematic preserves circle incidence, point order, and the named ray directions. Use the measures in the statement.TABORSSchematic; use the stated givens.
  12. 12

    VAVA is a diameter with center OO. Another point BB lies on the circle, and m∠VBO=32∘m\angle VBO=32^\circ. Find m∠AVBm\angle AVB.

    The center O lies on side VA of angle AVB; VA is a diameter.The center O lies on side VA of angle AVB; VA is a diameter. Exact angle and arc measures come from the statement; the schematic preserves the stated incidence and point order.VABOSchematic; use the stated givens.
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