ABCD is a kite with \(\angle A=46^\circ\) and \(\angle C=28^\circ\). Find the measure of \(\angle B\).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 143°
A kite has two pairs of equal adjacent sides, and the two angles between the unequal sides are equal. \(\angle A\) and \(\angle C\) are different (46° and 28°), so they are the angles where the equal sides meet (AB = AD, CB = CD), and the other two angles are equal: \(\angle B=\angle D\).
The angles of a quadrilateral add up to 360°: \(46^\circ+28^\circ+2\angle B=360^\circ\)
\(2\angle B=286^\circ\), so \(\angle B=143^\circ\)