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Find the measure of angle x in Figure 5.56, given the measures of intercepted arcs AC and BD.

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Question 1: Figure 5.56

The angle xx is formed by two chords intersecting inside a circle. The measure of an angle formed by two intersecting chords inside a circle is half the sum of the measures of the intercepted arcs. In this case, xx intercepts arc AC and arc BD.

  1. Identify the formula for the angle formed by two intersecting chords.

    x=12(m(arc AC)+m(arc BD))x = \frac{1}{2} (m(\text{arc AC}) + m(\text{arc BD}))

  2. Substitute the given arc measures.

    Given m(arc AC)=28∘m(\text{arc AC}) = 28^\circ and $m(arc BD) = 1

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