Mathematics

Question

Find the value of x for arc AB = 38° and arc CB = 25°.
Find the value of x for arc AB = 38° and arc CB = 25°.

2 Answer

  • x=38°
    Because the center angle is equal to the arc angle
  • Answer:

    [tex]\angle x=31.5^{\circ}[/tex]

    Step-by-step explanation:

    We have been given an image of a circle. We are asked to find the value of x.

    Upon looking at our given diagram, we can see that angle x is formed by intersection of chords BD and AC inside circle.

    To solve our given problem, we will use intersecting chords theorem, which states that the measure of an angle formed by two intersecting chords inside a circle is half the sum of intercepted arcs.

    Using intersecting chords theorem we can set an equation as:

    [tex]\angle x=\frac{\text{Measure of arc AB}+\text{measure of arc CD}}{2}[/tex]

    [tex]\angle x=\frac{38^{\circ}+25^{\circ}}{2}[/tex]

    [tex]\angle x=\frac{63^{\circ}}{2}[/tex]

    [tex]\angle x=31.5^{\circ}[/tex]

    Therefore, the value of x is 31.5 degrees.

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