Answer :

hackermcpe

Well first we need to remember that the measure of an inscribed angle is one half of its intercepted arc.

So use the following equation then solve

1/2xz = 72

Multiply each side by 2

xz = 144

144 is your answer

The relationship between the arc [tex]\widehat{XZ}[/tex] and the angle ∠XYZ is given by

circle theorems.

Correct response;

  • The measure of [tex]\widehat{XZ}[/tex] is; A. 144°

Method used for finding the arc [tex]\widehat{XZ}[/tex] of the circle

The given angle subtended by the arc [tex]\widehat{XZ}[/tex] = ∠XYZ = 72°

Required:

The measure of arc [tex]\widehat{XZ}[/tex]

Solution:

The measure of [tex]m\widehat{XZ}[/tex] = The angle subtended at the center by [tex]\widehat{XZ}[/tex]

m∠XYZ = The angle subtended by [tex]\widehat{XZ}[/tex] at the circumference

According to circle theorem, we have;

Angle subtended by an arc at the center = Twice the angle subtended by the arc at the circumference

Therefore;

  • [tex]m\widehat{XZ}[/tex] = 2 × ∠XYZ

Which gives;

[tex]m\widehat{XZ}[/tex] = 2 × 72° = 144°

  • [tex]\widehat{XZ}[/tex] is A. 144°

Learn more about circle theorems here:

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