Question

A circle is shown. Points Q, U, A, D are on the circle. Lines connect the points to form a quadrilateral. Angle Q U A is 111 degrees. Arc Q U is 88 degrees. What is the measure of Arc A U? 44° 50° 64° 92

Answer 1

Answer:

b. 50

Step-by-step explanation:

Answer 2

The angle subtended by an arc $\widehat{AU}$ is given by the angle ∠UOA.

Response:

• $\widehat{AU}$ is 50°

Which methods can be used to find $\widehat{AU}$ ?

According to circle theorem, we have;

• Angle at the center = 2 × Angle at the circumference

∠QUA = 111°

Therefore;

$m\widehat{QDA}$ = 2 × ∠QUA

$m\widehat{QDA}$ = 2 × 111° = 222°

Which gives;

Angle ∠QOA = $m\widehat{QUA}$ = 360° - 222° = 138°

∠QOA = ∠QOU + ∠UOA by angle addition property

Which gives;

∠QOA = 138° = 88° + ∠UOA

∠UOA = 138° - 88° = 50°

• $\widehat{AU}$ = ∠UOA = 50°

Learn more about more circle theorems here:

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