Question

in quadrilateral abcd, m∠d = 112. determine m∠b. enter the answer in the space provided. use numbers instead of words.

Explanation:

Step1: Recall cyclic quadrilateral property

In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the sum of opposite angles is \(180^\circ\). So, \(\angle D\) and \(\angle B\) are opposite angles.

Step2: Calculate \(m\angle B\)

Given \(m\angle D = 112^\circ\), we use the property \(m\angle D + m\angle B = 180^\circ\).

$$ m\angle B = 180^\circ - m\angle D $$

Substitute \(m\angle D = 112^\circ\) into the formula:

$$ m\angle B = 180^\circ - 112^\circ = 68^\circ $$

Answer:

\(68\)