Question

Quadrilateral $AEIU$ is inscribed in circle $O$. Given $m\angle A = 27^\circ$ and $m\angle E = 2(m\angle A)$, find $m\angle I$ and $m\angle U$.$m\angle I = 153^\circ$ and $m\angle U = 126^\circ$ $m\angle I = 153^\circ$ and $m\angle U = 153^\circ$$m\angle I = 126^\circ$ and $m\angle U = 153^\circ$$m\angle I = 126^\circ$ and $m\angle U = 126^\circ$

Answer 1

In a cyclic quadrilateral, opposite angles are supplementary. Since the vertices are A–E–I–U around the circle, A and I are opposite, and E and U are opposite.

Given m∠A = 27° and m∠E = 2·27° = 54°,

m∠I = 180° − m∠A = 180° − 27° = 153°,
m∠U = 180° − m∠E = 180° − 54° = 126°.

So m∠I = 153° and m∠U = 126°.